Total edge irregularity strength of the disjoint union of sun graphs

Muhammad Kamran Siddiqui, A Ahmad, M F Nadeem, Y Bashir

Abstract


An edge irregular total $k$-labeling $\varphi: V\cup E \to \{ 1,2, \dots, k \}$ of a~graph $G=(V,E)$ is a~labeling of vertices and edges of $G$ in such a~way that for any different edges $uv$ and $u'v'$ their weights $\varphi(u)+ \varphi(uv) + \varphi(v)$ and $\varphi(u')+ \varphi(u'v') + \varphi(v')$ are distinct. The total edge irregularity strength, $tes(G)$, is defined as the minimum $k$ for which $G$ has an~edge irregular total $k$-labeling. In this paper, we consider the total edge irregularity strength of the disjoint union of $\emph{p}$ isomorphic sun graphs, $tes(\emph{p}M_{n})$, disjoint union of $\emph{p}$ consecutive non-isomorphic sun graphs, $tes(\bigcup_{j=1}^{\emph{p}}M_{n_{j}})$.

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