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TOTAL OFFENSIVE ALLIANCE OF TOTAL GRAPHS GENERATED FROM GRAPHS WITH MAXIMUM DEGREE 2
Keywords:
total graph, offensive alliance, total offensive alliance, total offensive alliance numberDOI:
https://doi.org/10.17654/0974165825025Abstract
For a nontrivial connected graph $G=(V(G), E(G))$, a nonempty subset $T \subseteq V(G)$ is a total offensive alliance in $G$ if $T$ is an offensive alliance and every vertex in $T$ has at least one neighbor within $T$. The minimum cardinality of a total offensive alliance in $G$ is called the total offensive alliance number of $G$, denoted by $a_{t o}(G)$. In this paper, we investigate the total offensive alliance of total graphs generated from graphs with maximum degree 2 and present the characterization of total offensive alliance and their corresponding total offensive alliance number.
Received: February 7, 2025
Accepted: March 3, 2025
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