A New Graph over Semi-Direct Products of Groups

Sercan Topkaya, Ahmet Sinan Cevik


In this paper, by establishing a new graph $\Gamma (G)$ over the semi-direct product of groups, we will first state and prove some graph-theoretical properties, namely, diameter, maximum and minimum degrees, girth, degree sequence, domination number, chromatic number, clique number of $\Gamma (G)$. In the final section we will show that $\Gamma (G)$ is actually a perfect graph.

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