Total vertex product irregularity strength of graphs
نویسندگان
چکیده
Consider a simple graph $G$. We call 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 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 members $E(G)\cup V(G)$. minimum value $s$ that allows some irregular called \textit{the total vertex irregularity strength} and denoted $tvps(G)$. provide general bounds, as well exact values for chosen families graphs. Keywords: product-irregular labeling, strength, vertex-distinguishing labeling.
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2023
ISSN: ['1234-3099', '2083-5892']
DOI: https://doi.org/10.7151/dmgt.2495