Papers by SV Ashwin Prakash
Malaya Journal of Matematik, 2020
In this paper, we discuss about the irredundant number, upper irredundnat number and domination n... more In this paper, we discuss about the irredundant number, upper irredundnat number and domination number denoted by ir(G(n)), IR(G(n)) and γ(G(n)) respectively for 6-regular graphs of n vertices with girth 3. Here, G(n) denotes the 6-regular graphs on n vertices with girth 3. We further establish some relation between ir(G(n)), IR(G(n)) and γ(G(n)).
Malaya Journal of Matematik, 2020
In this paper, we introduce the concept detour global domination number of a graph. Also detour g... more In this paper, we introduce the concept detour global domination number of a graph. Also detour global domination number of certain classes of graphs are determined and some of its general properties are studied. A set S of vertices in a connected graph G = (V, E) is called a detour set if every vertex not in S lies on a longest path between two vertices from S. A set D of vertices in G is called a dominating set of G if every vertex not in D has at least one neighbor in D. A set H ⊆ V (G) is called a global dominating set of G if it is a dominating set of both G and G. A set S is called a detour global dominating set of G if S is both detour and global dominating set of G. The detour global domination number is the minimum cardinality of a detour global dominating set in G.
Discrete Mathematics, Algorithms and Applications
In this paper, we introduced the new concept detour global domination number for splitting graph ... more In this paper, we introduced the new concept detour global domination number for splitting graph of standard graph. The detour global dominating sets in some standard and special graphs are determined. First we recollect the concept of splitting graph of a graph and we produce some results based on the detour global domination number of splitting graph of star graph, bistar graph and complete bipartite graph. A set [Formula: see text] is called a detour global dominating set of [Formula: see text] if [Formula: see text] is both detour and global dominating set of [Formula: see text]. The detour global domination number is the minimum cardinality of a detour global dominating set in [Formula: see text].
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Papers by SV Ashwin Prakash