International Journal of Mathematics and Soft Computing

7

Authors: B. Gayathri, R. Gopi

In this paper, we introduce the concept of $(k, d)$-even mean labeling and investigate $(k, d)$-even mean labeling of $P_m\odot nK_1$.

8

Authors: KM. Kathiresan, G. Marimuthu, C. Parameswaran

For distinct vertices u and v of a nontrivial connected graph G, we let Du,v = N[u] [ N[v]. We define a Du,v-walk as a u-v walk in G that contains every vertex of Du,v. The superior distance dD(u, v) from u to v is the length of a shortest Du,v-walk. For each vertex u 2 V (G), define d−D(u) = min{dD(u, v) : v 2 V (G) − {u}}. A vertex v(6= u) is called a superior neighbor of u if dD(u, v) = d−D(u). In this paper we define the concept of superior complement of a graph G as follows: The superior complement of a graph G is denoted by GD whose vertex set is as in G. For a vertex u, let Au = {v 2 V (G) : dD(u, v)  d−D(u) + 1}. Then u is adjacent to all the vertices v 2 Au in GD. The main focus of this paper is to prove that there is no relationship between the superior diameter dD(G) of a graph G and the superior diameter dD(GD) of the superior complement GD of G.

8

Authors: S.Balamurugan, A. Wilson Baskar,V. Swaminathan

A subset $D$ of a vertex set $V$ of a graph $G$ is a chromatic strong dominating set if $D$ is a strong dominating set and $\chi()=\chi(G)$. \ \ The minimum cardinality of chromatic strong dominating set is called chromatic strong domination number of $G$ and is denoted by $\gamma_{s}^c(G)$. In this paper we study relationship between strong domination and chromatic strong domination of a graph.

10

Authors: P. Lawrence Rozario Raj, S. Koilraj

In this paper we prove that the splitting graph of path Pn, cycle Cn, complete bipartite graph Km,n, matching Mn, wheel Wn and are cordial.

12

Authors: Sr. Kulrekha, R. Sundareswaran, V. Swaminathan

The hamiltonian coloring of a connected graph $G$ introduced by Chartrand et al \cite {ch} is different from hamiltonian partition coloring. In this paper, we characterize graphs which has a hamiltonian partition. Also, we give example of graphs having prescribed chromatic numbers and hamiltonian partition numbers. We derive results connecting the hamiltonian chromatic number of $G_1 \cup G_2$ and $G_1 + G_2$.

15

Authors: K. Murugan, A. Subramanian

A graph G(V,E) with p vertices and q edges is said to have skolem difference mean labeling if it is possible to label the vertices xV with distinct elements f(x) from 1,2,3…p+q in such a way that the edge e=uv is labeled with if |f(u)-f(v)| is even and if |f(u)-f(v)| is odd and the resulting edges get distinct labels from 1,2,3…q. A graph that admits skolem difference mean labeling is called skolem difference mean graph.