A Study On Domination In Lower deg-centric graphs

Abstract

The lower deg-centric graph of a simple connected graph $G$, denoted by $G_{ld}$, is a graph constructed from $G$ such that $V(G_{ld}) = V(G)$ and $E(G_{ld}) = \{v_iv_j: d_G(v_i,v_j)< deg_G(v_i)\}$. A dominating set in a graph $G$ with vertex set $V(G)$ is a set $S$ of vertices of $G$ such that every vertex in $V(G)-S$ is adjacent to at least one vertex in $S$. The domination number of $G$, denoted by $\gamma(G)$, is the minimum cardinality of a dominating set of $G$. This paper presents the domination properties and
domination number of lower deg-centric graphs. In addition, investigate the properties and structural characteristics of this type of graph.