SUPERLATIVE TOTAL DOMINATION IN GRAPHS | ||||
| Electronic Journal of Mathematical Analysis and Applications | ||||
| Volume 12, Issue 1, January 2024, Page 1-10 PDF (493.63 K) | ||||
| Document Type: Regular research papers | ||||
| DOI: 10.21608/ejmaa.2024.220095.1043 | ||||
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| Authors | ||||
Chaluvaraju B   1; VEENA BANKAPUR 2
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| 1Department of Mathematics, Jnanabharathi Campus, Bangalore University, BENGALURU 560 056 | ||||
| 2Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bangalore -560 056, India | ||||
| 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 | ||||
| Domination; Inverse domination; Total domination; Maximal total domination; Superlative total domination | ||||
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