International Journal of Mathematics and Soft Computing

5-9

Authors: M. Valliammal, S. P. Subbiah, V. Swaminathan

Let $G=(V,E)$ be a graph without isolates. A subset $S$ of $V(G)$ is called a total dominating set of $G$ if for every $v\in V$, there exists $u\in S$ such that $u$ and $v$ are adjacent. $S$ is called a total complementary acyclic dominating set of $G$, if $S$ is a total dominating set of $G$ and $\left\langle V-S\right\rangle$ is acyclic. $V(G)$ is a total complementary acyclic dominating set of $G$ (since $G$ has no isolates). The minimum cardinality of a total complementary acyclic dominating set of $G$ is called the total complementary acyclic domination number of $G$ and is denoted by $\gamma_{c-a}^{t}(G)$. In this paper, characterization of graphs for which $\gamma_{c-a}^{t}(G)$ takes specific values are found.

17-20

Authors: S. Balamurugan, G. Prabakaran

A dominating set D of graph G = (V, E) is a disconnected dominating set, if the induced subgraph < D > is disconnected. The disconnected dominating number (G) of G is the minimum cardinality of a disconnected dominating set of G. In this paper, we relate this parameter to other parameters of graph G and obtain some bounds also. dc 

27-35

Authors: R. B. Gnana Jothi, A. Uma Devi

A graph G = (V, E) is said to be topogenic if it admits a topogenic set indexer, which is a set indexer f: V 2X such that f(V) is a topology on X. A list colouring of a graph G = (V,E) with a colour list C = for V = {v1, v2, ….vn} is a proper colouring of V by element of so that the adjacent vertices u,v are coloured differently and the colour for is in C(V). L- edge colouring of a graph G is an assignment L:E(G)2X- such that no two adjacent edges receive the same label where X is a ground set. A graph G is to be L- edge colourable if there exists an L- edge colouring of G. A comparative study of topogenic graphs and L- edge colourable graphs has been made in this paper.

41-48

Authors: N. Meena, A. Subramanian, V. Swaminathan

A subset S of V(G) of a graph G is called a strong (weak) efficient dominating set of G if for every v ∈ V(G), │Ns[v]∩S│= 1 (│Nw[v]∩S│= 1 ) where Ns(v) = { u ∈ V(G) : uv ∈ E(G), deg(u) ≥ deg(v) } and Nw(v) = { u ∈ V(G) : uv ∈ E(G), deg(v) ≥ deg(u)}, Ns[v] = Ns(v) ∪ {v}, Nw[v] = Nw(v) ∪ {v}. The minimum cardinality of a strong (weak) efficient dominating set is called strong (weak) efficient domination number of G and is denoted by γse (G) (γwe (G)). A graph G is strong efficient if there exists a strong efficient dominating set.