Bulletin of the International Mathematical Virtual Institute

11-21

Authors: Muhammad Sarwar, Mian Bahadur Zada and Saurabh Manro

In this paper, using the (CLR) and (E:A) properties of the involved pairs, common fixed point results for four and six weakly compatible self-mappings are established in complex valued metric spaces. Our results include some known results as special cases.

31-41

Authors: K. Pattabiraman and M. Vijayaragavan

For a (molecular) graph, the hyper Zagreb index is defined as HM(G) = Σuv2E(G) (dG(u) + dG(v))2 and the hyper Zagreb coindex is defined as HM(G) = Σ uv=2 E(G) (dG(u)+dG(v))2: In this paper, the hyper Zagreb indices and its coindices of edge corona product graph, double graph and Mycielskian graph are obtained.

53-63

Authors: B. Chaluvaraju and V. Chaitra

In this paper, we newly constructed the sign dominating outer (inner) switched graph mio d(G) (mii d(G)) of a graph G = (V;E) and establish their properties. Also we determine number of edges and its relation between mio d(G) and mii d(G) in some special classes of graphs are explored.

73-83

Authors: Akram Alqesmah, Anwar Alwardi and R. Rangarajan

Let G = (V;E) be a connected graph. A subset S of V is called injective dominating set (Inj-dominating set) if for every vertex v 2 V

93-102

Authors: R.D. Jagatap and Y.S. Pawar

In this paper we introduce the concepts of prime, semiprime, strongly prime, irreducible and strongly irreducible bi-ideals in a Г-semiring. Characterizations of a Г-semiring using these concepts are furnished. A topology on the set of strongly prime bi-ideals is defined and a property of the space of strongly prime bi-ideals of a Г-semiring is furnished.

117-128

Authors: Nilanjan De

The Narumi-Katayama index of a graph G is equal to the product of degrees of all the vertices of G. In this paper, we examine the Narumi- Katayama index of some derived graphs such as a Mycielski graph, subdivision graphs, double graph, extended double cover graph, thorn graph, subdivision vertex join and edge join graphs.

139-151

Authors: O. Ravi, P. Sekar and K. Vidhyalakshmi

In this paper, we introduce some generalizations of !-open sets in ideal topological spaces and investigate some properties of the sets. Moreover, we use them to obtain decomposition of continuity via idealization.

165-171

Authors: Adara M. Blaga

In the context of para-Kenmotsu geometry properties of the generalized dual connections of some canonical linear connections (Levi-Civita, para-Kenmotsu canonical, Golab and Zamkovoy canonical paracontact connections) are established.

181-191

Authors: Ahmed A. Abdelhakim and R. A. Rashwan

We prove strong convergence of an implicit iteration procedure equipped with error terms to the solution of a system involving total asymptotically non-expansive mappings, in uniformly convex Banach spaces.

135-141

Authors: Omur Kivanc Kurkcu and Huseyin Aksan

The vulnerability shows the resistance of the network until com- munication breakdown after the disruption of certain stations or communi- cation links. This study introduces a new vulnerability parameter, neighbor toughness. The neighbor toughness of a graph G is dened as NT(G) = minf jSj !(G=S) : !(G=S) > 1g, where S is any vertex subversion strategy of G and !(G=S) is the number of connected components in the graph G=S. In this paper, the relations between neighbor toughness and other parameters are determined and the neighbor toughness of some specic graphs are obtained.

157-167

Authors: M. Kamal Kumar, R. Murali and V. Chidanandan

Domination and other related concepts in undirected graphs are well studied. Although domination and related topics are extensively studied, the respective analogies on digraphs have not received much attention. Such studies in the directed graphs have applications in game theory and other areas. A directed graph D is a pair (V;E), where V is a non empty set and E is a set of ordered pairs of elements taken from set V . V is called vertices and E set called directed edges. Let D = (V;E) be a digraph if (x; y) 2 E then arc is directed from x to y and is denoted by x ! y. The vertex x is called a predecessor of y and y is called a successor of x. A set S  V of a digraph D is said to be a dominating set of D if 8v =2 S, v is a successor of some vertex s 2 S. In this paper we study domination theory on few well known classes of directed trees. Directed trees are extensively used in path algorithm, scheduling problems, data processing networks, data compression, causal structures like family tree, Bayesian network, moral graphs, in uence diagram etc. The concept of dominating function plays a signicant role in these models.

181-188

Authors: Pankaj Kumar Jhade, R.A.Rashvan and A.S.Saluja

The aim of this paper is to prove a coincidence point theorem for a class of self mappings satisfying nonexpansive type condition under various conditions and a xed point theorem is also obtained. Our results extend and generalizes the corresponding result of Singh et al. [7].

199-208

Authors: Adesanmi Alao Mogbademu

In this paper, we prove some strong convergence theorems of the modified Mann iteration with errors for a new class of nonlinear mappings in real Banach spaces. Our results not only employ a simple proof technique, but also extend some well known results in this area of research.

219-226

Authors: Aleksandr Tsarev, Tongsuo Wu and Artem Lopatin

Let $\tau$ be a subgroup functor (in Skiba's sense) such that all subgroups of any finite group $G$ contained in $\tau(G)$ are subnormal in $G$. In this paper, we show first that the lattice of all $\tau$-closed $n$-multiply composition formations of finite groups $\mathcal C_n^\tau$ is not distributive for every non-negative integer $n$. Next, we prove that if $\mathfrak F \neq (1)$ is a non-empty $\tau$-closed $n$-multiply composition formation then its $\tau$-closed Frattini subformation $\Phi_n^\tau(\mathfrak F)$ consists of all $\mathcal C_n^\tau$-non-generating groups of $\mathfrak F$. Moreover, if $\mathfrak F_1$ is a $\tau$-closed $n$-multiple composition subformation of $\mathfrak F$ then $\Phi_n^\tau(\mathfrak F_1) \subseteq \Phi_n^\tau(\mathfrak F)$.

241-249

Authors: K. M. Nagaraja, P. Siva Kota Reddy and K. Sridevi

Convexity/Concavity nature of different means are generally dis-cussed. But in this paper relative study of convexity/Concavity between different means are found and these results are interpreted in Van der Monde determinants.

259-267

Authors: Daniel A. Romano

This investigation is in the Bishop's constructive mathematics. We discuss about co-order, co-quasiorder and coequality relations on set X with appartness. A connection between the family of all co-quasiorder relations and the family of all coequality relations on set X is given. In addition, a connection between the family of all co-quasiorder relations included in the co-order  and the family of all regular coequality relation on X with respect to  is also given.

13-24

Authors: Anwar Alwardi and P.M.Shivaswamy

Graph polynomials are polynomials associated to graphs that en-code the number of subgraphs with given properties. In this paper we introduce a new type of graph polynomial called neighbourhood polynomial. We obtained the neighbourhood polynomial of some interested standard graphs like complete graph, complete bipartite graph, bi-star graph, spider, wounded spider graph and for some corona product graphs.

37-48

Authors: Harina O. L. Monim, Indah E. Wijayanti and Sri Wahyuni

In the framework of fuzzy sets and corresponding techniques, we investigate functions from a nonempty set X into an ordered structure (S;6) where S is a meet-semilattice.Each function mi : X ! S determines a family of subsets of X, which are called cut sets. Vice versa, particular family of subsets of X, indexed by the elements of S uniquely determines a function from X to S. Further, any function  : X ! S determines a semi-closure operator on S, which induces an equivalence relation on the semilattice S. Using the above results, we classify functions in SX.

55-64

Authors: Saadet Eskiizmirliler, Goksen Bacak-Turan and Refet Polat

A vertex subversion strategy of a graph G, say S, is a set of vertices in G whose closed neighborhood is removed from G. The survival subgraph is denoted by G=S. The neighbor rupture degree of G is dened to be Nr(G) = maxfw(G=S)

77-87

Authors: Fuad S. Al Sarari and S. Latha

In this note, the concepts of (j; i)-symmetric points, Janowski functions and the conic regions are combined to define a class of functions in a new interesting domain which represents the conic type regions. Certain interesting coeficient inequalities are deduced.

97-104

Authors: Tabitha Agnes M., L. Sudershan Reddy, Joseph Varghese K., and John Stephen Mangam

The diametral path of a graph is the shortest path between two vertices which has length equal to diameter of that graph. Diametral path decomposition is introduced as a collection of edge-disjoint diametral paths of a graph so that every edge of the graph appears in exactly one diametral path. Diametral path decomposition number de is the cardinality of such a collection. The diametral path decomposition index De is the number of such decompositions. In this paper, results on de and De in some classes of graphs are presented. Also graphs which admit diametral path decomposition are charecterized.

115-125

Authors: K.P.R.Rao, Sk. Sadik and S.Manro

In this paper, we obtain a unique common fixed point theorem for four self maps satisfying rational ( ; ϕ; φ)-contractive condition using - admissible function in ordered partial metric spaces. Also we give an example to illustrate our main theorem.

115-124

Authors: Pankaj Kumar Jhade , A.S. Saluja and M.S.Khan

Let C be a closed convex weakly Cauchy subset of a normed space X. Then we dene new fa; b; cg-type generalized nonexpansive mapping and fa; b; cg-type generalized contraction mapping T from C into C. These type of mappings will be denoted respectively by fa; b; cg-gntype and fa; b; cg-gctype. The aim of this paper is to establish some strong convergence results for such type of mappings. Our results extends and generalizes some of the results given in [2].

133-140

Authors: Duško Bogdanić

In this paper we show that tame blocks of group algebras with semidihedral defect groups and two isomorphism classes of simple modules can be non-trivially graded. We prove this by using the transfer of gradings via derived equivalences.

153--158

Authors: J.Chithra, S.P.Subbiah and V.Swaminathan

Adin and Roichman introduced the concept of permutation graphs and Peter Keevash, Po-Shen Loh and Benny Sudakov identified some permutation graphs with maximum number of edges. Charles J Colbourn, Lorna K.Stewart characterized the connected domination and Steiner Trees under the Permutation graphs. If i, j belong to a permutation  on p symbols A = {1, 2, , p} and i < j then the line of i crosses the line of j in the permutation if i appears after j in the image sequence s() and if the no. of crossing lines of i is less than the no. of crossing lines of j then i strongly dominates j. A subset D of A, whose closed neighborhood is A in  is a dominating set of . D is a strong dominating set of  if every i in A−D is strongly dominated by some j in D. In this paper the strong number of a permutation is investigated by means of crossing lines.

165-169

Authors: Daniel A. Romano

In article [4], quasi-regular relations and dually quasi-regular re- lations on sets are introduced and analyzed. In this paper, following Jiang Guanghao and Xu Luoshan's concepts of finitely conjugative and finitely dual normal relations on sets, the concept of finitely dual quasi-regular relations is introduced, as a continuation of [4]. Characterizations of finitely dual quasi- regular relations are obtained.

181-190

Authors: R. Ponraj and S.Sathish Narayanan

A total mean cordial labeling of a graph G = (V,E) is a function f : V (G) ! {0, 1, 2} such that for each edge xy assign the label l f(x)+f(y) 2 m where x, y 2 V (G) and  evf (i) − evf (j) 6 1, i, j 2 {0, 1, 2} where evf (x) denotes the total number of vertices and edges labeled with x (x = 0, 1, 2). If there exists a total mean cordial labeling on a graph G, we will call G is total mean cordial. In this paper, we investigate the total mean cordial labeling behavior of some derived graphs.

197-204

Authors: Puttaswamy and Mohammed Alatif

Let G = (V;E) be a connected graph, A subset S of E(G) is called a boundary edge dominating set if every edge of E

13-23

Authors: Sabbavarapu Nageswara Rao

We determine intervals for two eigenvalues for which there exists no positive solution of a system of nonlinear higher-order ordinary differential equations (

33-36

Authors: Igor Milovanović and Emina Milovanović

We have dened a new class of convex sequences, referred to as Lkp -convex sequences. These sequences represent generalization of a class of k-convex sequences, k > 2. Some important properties of Lkp -convex sequences are proved.

47-55

Authors: N. Rafi, Ravi Kumar Bandaru and G.C. Rao

In this paper two kinds of congruences are proposed in an Almost distributive lattice(ADL), rst one is considered in terms of ideals generated by derivations and second one is followed by in terms of images of derivations. An equivalent condition is derived for the corresponding quotient ADL to become a Boolean algebra. An another equivalent condition is also established for the existence of a derivation.

65-72

Authors: Mukaddes Ökten Turaci and Turgut Özis

Recently, the Runge-Kutta methods, obtained via Taylor's expan- sion is exist in the literature. In this study, we have derived explicit methods for problems of the form y0 = f(y) including second and third derivatives , by considering available Two-Derivative Runge-Kutta methods (TDRK). The methods use one evaluation of rst derivative, one evaluation of second de- rivative and many evaluations of third derivative per step. The methods can be named as Three- Derivative Runge-Kutta methods, ThDRK shortly. We present methods with stages up to three and order up to seven. Comparisons is made with other some existing methods on some standard problems. The stability region of the methods are given.

81-88

Authors: K.M.Dharmalingam, R.Udaya Suriya and P.Nithya

Let G be a fuzzy graph. Let u and v be two vertices of G. A subset D of V is called a fuzzy equitable dominating set if every v 2 V

95-102

Authors: Vecdi Aytac and Sema Bodur

Vulnerability concerns the issue of network robustness to mali- cious attacks. Many complex systems in the real world can be conceptually described as networks, where nodes represent the system constituents and edges depict the interaction between them. Often enough, the network rep- resentation of these systems is an undirected and unweighted graph which greatly simplies the structure of complex systems. If we think of a graph as modeling a network, then we have some graph parameters to measure the vulnerability, including connectivity, toughness, binding number, domination number and integrity. In this paper, we consider the integrity and strong dom- ination numbers as vulnerability measures. We determine the integrity and strong domination numbers of splitting graphs S′(G) for specic graphs G.