Bulletin of the International Mathematical Virtual Institute

401-412

Authors: Burak Kaval and Alpay Kirlangic

In a communication network, the vulnerability is the resistance of the network to disruption of operation after the failure of certain stations or communication links. If a communication network was modelled by a graph, then the scattering number measures vulnerability of the graph. The scattering number of an arbitrary graph G = (V;E) is defined to be sc(G) = maxf!(G

203-212

Authors: Dilek Bayrak and Sultan Yamak

In this paper, we investigated concept of TL-vague module and obtained some basic properties of this concept.

221-231

Authors: Murat Düz

In this study, second order linear complex differential equations are solved by the Adomian decomposition method. A theorem is given for this method. Furthermore some examples are given, and the results obtained indicate this approach is indeed practical.

245-258

Authors: R. Ponraj, M. Maria Adaickalam and R. Kala

Path, complete graph, difference cordial, corona

271--278

Authors: Aysun Ayatac and Betul Atay

The assessment of the stability and the vulnerability of complex networks is the important concept while studying of them. In the literature, a sort of measures have been given in order to assessment the stability of systems. And also, some graph-theoretic parameters have been formed to provide formulas which calculate the reliability of a network. In this paper, we study the vulnerability of some cycles and related graphs to the dominating strategy of a vertex, using a measure called exponential domination number which is a new characteristic for graph vulnerability.

287-299

Authors: Waleed Mohd. Alfaqih, Mohammad Imdad, and Rqeeb Gubran

The aim of this paper is to discuss the existence and uniqueness of a common solution for the following system of linear Fredholm integral equations (of the second kind) where beta in R, fi; Ki and Fi are given continuous functions, i = 1; 2 while u is unknown function to be determined. To establish this, we prove a common fixed point theorem for two self-mappings defined on a complex metric space. Moreover, we prove coincidence and common fixed point theorems for two weakly compatible self-mappings defined on a complex metric space.

315-323

Authors: R. Rajkumar and S. Celine Prabha

Let Pn be the path graph on n vertices. In this paper, we consider the distance graphs G(Pn;D), where the distance set D  f1; 2; 3; : : : ; n

337-344

Authors: Fikret Čunjalo

In the [3] is proven that sequence Sij uniformly statistically converges to L if and only if it there is a subset A of the set N  N uniform density zero and subsequence S (x) dened by, Sij (x) = Sij for (i; j) 2 Ac, converges to L, in the Pringsheim's sense. In this paper it is proven that analog is valid for subsequence S (x) provided that for each N and i 6 N _ j 6 N is a set of all Sij (x) nite set. Is generally valid: If the subsequence S (x) uniformly statistically converges to L, then, there is a subset A of the set N  N uniform density zero and subsequence S (y) dened by, Sij (y) = Sij (x) for (i; j) 2 Ac, converges to L, in the Pringsheim's sense. If there is a subset A of the set N  N uniform density zero and subsequence S (y) dened by, Sij (y) = Sij (x) for (i; j) 2 Ac, such that limi!1( limj!1Sij (y)) = L, then, the subsequence S (x) uniformly statistically converges to L.

357-364

Authors: Noorbhasha Rafi and Ravi Kumar Bandaru

The concept of extended ideals in an Almost distributive Lattice is introduced and studied their properties.

369-383

Authors: Ali Ghalavand, Ali Reza Ashra and Ivan Gutman

Let G be a graph with edge set E(G). The second multiplicative Zagreb index of G is defined as 2(G) = Π uv2E(G)[degG(u) degG(v)], where degG(v) is the degree of the vertex v of G. In this paper, the unicyclic graphs with rst through seventh smallest 2

391-396

Authors: Naveen Kumar Kakumanu, G.C. Rao and Kar Ping Shum

In this paper, we introduce the concept of a Factor Almost Distributive Lattice and derive some of its important properties. We also prove that if I is an ideal of B then the Factor Almost Distributive Lattice A=I is a Post Almost Distributive Lattice.

1-9

Authors: R. Ponraj and Rajpal Sings

Let G be a (p; q) graph. Let f : V (G) ! f1; 2; : : : ; kg be a function. For each edge uv, assign the label gcd (f(u); f(v)). f is called k-prime cordial labeling of G if  vf (i)

21-35

Authors: Arzu Denk Oguz and Fatma Serap Topal

By employing the Schauder's fixed point theorem, we study the existence of positive solutions for a singular semipositone dynamic system on time scales. New existence results are established, which is in essence different from the known results.

45-53

Authors: M. Murali Krishna Rao

In this paper, we introduce the notion of left (right) bi-quasi ideal and bi-quasi ideal of semiring which are generalizations of bi-ideal and quasi ideal of semiring. Also we study the properties of bi-quasi ideals, left bi-quasi ideals and characterize the left bi-quasi simple semring and regular semiring.

67-80

Authors: P. Jeyanthi and T. Saratha Devi

An injective map f : E(G) ! f1;2;


;qg is said to be an edge pair sum labeling of a graph G(p; q) if the induced vertex function f : V (G) ! Z

89-97

Authors: R.Ponraj, Rajpal Singh and R. Kala

Let G be a (p, q) graph. Let f : V (G) ! {1, 2, . . . , k} be a function. For each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of G if  vf (i) − vf (j) 6 1, i, j 2 {1, 2, . . . , k} and  ef (0) − ef (1) 6 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1. A graph with admits a k-prime cordial labeling is called a k-prime cordial graph. In this paper we investigate 4-prime cordial labeling behavior of union of two bipartite graphs, union of trees, durer graph, tietze graph, planar grid Pm × Pn, subdivision of wheels and subdivision of helms.

113-122

Authors: Edward Neuman

Optimal inequalities involving the p-Yang means are established. Bounding quantities are either the arithmetic or geometric or the harmonic combinations of the p-geometric and the p-quadratic means.

135-143

Authors: Arslan Hojat Ansari and Rajinder Sharma

This study deals with an establishment of some common xed point theorems for weak sub sequential continuous and compatibility of type (E) maps via C-class functions in a non Archimedean Menger Probabilistic Metric space.

155-159

Authors: Rakshith B. R.

In this note, we give an upper bound for degree distance index of a graph in terms of vertex Padmakar-Ivan index, rst Zagreb index, diameter and number of triangles. Also, we give a lower bound for degree distance index of a graph in terms of vertex Padmakar-Ivan index and number of triangles.

169-176

Authors: P Muralikrishna and D Vijayan

This paper discuss Fuzzy SU-ideal Topological Structure on SU-algebras, by connecting the two notions SU-algebras and Fuzzy Topology.

189-202

Authors: Marapureddy Murali Krishna Rao

In this paper we study the properties of structures of the semi-group (M; +) and the G-semigroup M of field G-semiring M, totally ordered G-semiring M and totally ordered field G-semiring M satisfying the identity a + ab = a for all a; b 2 M;  2