International Journal of Mathematics and Soft Computing

1-5

Authors: S K Vaidya, N J Kothari

In this paper we determine the distance k-domination number for splitting graph of path as well as the graphs obtained by duplication of a vertex by an edge and duplication of an edge by a vertex.

17-25

Authors: M Javaid

This paper deals with the construction of generalized extended w-trees denoted by $GEwt(n,m,r,k)$ and the existence of a super $(a,d)$-edge-antimagic total labeling on them for $d\in\{0, 1, 2\}$.

35-49

Authors: Pious Missier, Anto Kinsley, Evangeline Prathibha Fernando

Dominating sets are used in the allocation of finite resources to massively parallel architectures. In this paper, we propose a new way of determining a minimal dominating set, connected dominating set and total dominating set of an extended star graph ES (n, k) as well as the extended star graph with cross-connections ESC (n, k) using the levels of its architecture instead of nodes thereby reducing the running time of a domination algorithm significantly.

61-66

Authors: P O Ochieng, A W Manyonge, Andrew O Oduor

In this paper we estimate the value of tip speed ratio of a wind turbine and evaluate its effects on power coefficient. The power coefficient, $C_p$, is achieved at a particular tip speed ratio, $\beta$, which is specific to the design of the turbine.

73-80

Authors: M Javaid, Sajid Mahboob, Abid Mahboob, M Hussain

Labeling is an interesting technique to assign labels to vertices and edges of a graph under certain conditions. There are many types of labeling, for example magic, antimagic, graceful, odd graceful, cordial, radio, sum and mean labeling. This paper deals with different results related to $(a,d)$-edge-antimagic total and super $(a,d)$-edge-antimagic total labelings of a subclass of subdivided stars denoted by $T(n,n+2,n+5,2n+7,n_5,...,n_r)$, where $n\equiv 1\hphantom{a}(\mbox{mod}\hphantom{a}2)$, $n_m=2^{m-3}(n+3)+1$ and $5\leq m\leq r$.

93-101

Authors: S K Vaidya, Lekha Bijukumar

A graph $G=(V(G),E(G))$ with $p$ vertices and $q$ edges is said to be an \textit{odd sequential graph} if there is an injection $f:V(G)\rightarrow\{0,1,\ldots,q\}$ or if $G$ is a tree then $f$ is an injection $f:V(G)\rightarrow\ {0,1,\ldots,2q-1\}$ such that when each edge $xy$ is assigned the label $f(x)+f(y)$, the resulting edge labels are $\{1,3,...,2q-1\}$. In this paper we investigate some new families of odd sequential graphs. We also introduce two new concepts namely bi-odd sequential graphs and global odd sequential graphs and some of their characteristics are discussed.

113-118

Authors: D. K Thakkar, Ashish Amrutlal Prajapati

In this paper we study the effect of removing a vertex from the semigraph on strong vertex covering number and strong independence number. Also we prove that the strong vertex covering number does not increase when a vertex is removed from the semigraph.

129-137

Authors: T Tharmaraj, P. B Sarasija

A ( p, q) graph G(V, E) is said to be a square graceful graph if there exists an injection f :V(G)→{0,1,2,3,..., q2 } such that the induced mapping f p : E(G) → {1, 4, 9,..., q2} defined by f (uv) | f (u) f (v) | p = − is a bijection. The function f is called a square labeling ofG. In this paper, we prove that the star n K 1, , bistarm n B , , the graph obtained by the subdivision of the edges of the star K1,n , the graph obtained by the subdivision of the central edge of the bistar Bm,n, the generalised crown n C K 3 1, Θ , graph 1 P nKmΘ(n ≥ 2) , the comb 1 P K nΘ, graph ( , ) m n P S , (3, t) kite graph (t ≥ 2) and the path Pnare square graceful graphs.

145-153

Authors: Selvam AvadayappanR Sinthu

For every assignment f: V(G)→{0, 1, 2, . . . , q}, an induced edge labeling f* : E(G) → {1, 2, 3, . . . , q}is defined by 2 f (u) + f (v) if f (u) and f (u) are of same parity and by 2 f(u) + f (v) +1 otherwise for every edge uv∈E (G). If f *(E) = {1, 2, 3, . . . , q} , then we say that f is a mean labeling of G. If a graph G admits a mean labeling, then G is called a mean graph. In this paper, we prove that the graphs Cn+v1v3 (n≥4), C2(Pn), n≥2, Tn(Cm), n ≥ 2, m≥3,DQ(n), n ≥ 2, TQ(n), n ≥ 2 and mCn– snake, m ≥ 1, n ≥ 3 are mean graphs.