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arXiv · 1912.12136

Total vertex product irregularity strength of graphs

Marcin Anholcer·Azam Sadat Emadi·Doost Ali Mojdeh
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Abstract

Consider a simple graph $G$. We call a labeling $w:E(G)\cup V(G)\rightarrow \{1, 2, \dots, s\}$ (\textit{total vertex}) \textit{product-irregular}, if all product degrees $pd_G(v)$ induced by this labeling are distinct, where $pd_G(v)=w(v)\times\prod_{e\ni v}w(e)$. The strength of $w$ is $s$, the maximum number used to label the members of $E(G)\cup V(G)$. The minimum value of $s$ that allows some irregular labeling is called \textit{the total vertex product irregularity strength} and denoted $tvps(G)$. We provide some general bounds, as well as exact values for chosen families of graphs. Keywords: product-irregular labeling, total vertex product irregularity strength, vertex-distinguishing labeling.

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Marcin Anholcer, Azam Sadat Emadi, Doost Ali Mojdeh. 2019-12-27. Total vertex product irregularity strength of graphs. https://arxiv.org/abs/1912.12136

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