SUPERLATIVE TOTAL DOMINATION IN GRAPHS

B, Chaluvaraju; BANKAPUR, VEENA

doi:10.21608/ejmaa.2024.220095.1043

SUPERLATIVE TOTAL DOMINATION IN GRAPHS

Document Type : Regular research papers

Authors

Chaluvaraju B ¹
VEENA BANKAPUR ²

¹ Department of Mathematics, Jnanabharathi Campus, Bangalore University, BENGALURU 560 056

² Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bangalore -560 056, India

10.21608/ejmaa.2024.220095.1043

Abstract

Let $G = (V, E)$ be a simple graph with no isolated vertices and $p\geq 3$. A set $D\subseteq V$ is a dominating set, abbreviated as $DS$, of a graph $G$, if every vertex in $V-D$ is adjacent to some vertex in $D$, while a total dominating set, abbreviated as $TDS$, of $G$ is a set $T\subseteq V$ such that every vertex in $G$ is adjacent to a vertices in $T$. A set $T$ is a superlative total dominating set, abbreviated as $STDS$, of a graph $G$ if $V - T$ is not contains a $TDS$ but it contains a $DS$ of $G$. The superlative total domination number $\gamma_{st}(G)$ is the minimum cardinality of a $STDS$ of a graph $G$. In this paper, we initiate a study on $\gamma_{st}(G)$ and its exact values for some classes of graphs. Furthermore, bounds in terms of order, size, degree and other domination related parameters are investigated.

Keywords