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arXiv · 1707.02039

A note on some variations of the $\gamma$-graph

C. M. Mynhardt·L. E. Teshima
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Abstract

For a graph $G$, the $\gamma$-graph of $G$, $G(\gamma)$, is the graph whose vertices correspond to the minimum dominating sets of $G$, and where two vertices of $G(\gamma)$ are adjacent if and only if their corresponding dominating sets in $G$ differ by exactly two adjacent vertices. In this paper, we present several variations of the $\gamma$-graph including those using identifying codes, locating-domination, total-domination, paired-domination, and the upper-domination number. For each, we show that for any graph $H$, there exist infinitely many graphs whose $\gamma$-graph variant is isomorphic to $H$.

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C. M. Mynhardt, L. E. Teshima. 2017-07-07. A note on some variations of the $\gamma$-graph. https://arxiv.org/abs/1707.02039

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