Total Vertex Irregularity Strength of the Disjoint Union of Sun Graphs

Abstract

A vertex irregular total $k$-labeling of a graph $G$ with vertex set $V$ and edge set $E$ is an assignment of positive integer labels $\{1,2,...,k\}$ to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of $G$, denoted by $tvs(G)$ is the minimum value of the largest label $k$ over all such irregular assignment. In this paper we consider the total vertex irregularity strengths of disjoint union of $s$ isomorphic sun graphs, $tvs(sM_n)$, disjoint union of $s$ consecutive non-isomorphic sun graphs, $tvs(\bigcup_{i=1}^sM_{i+2})$, and disjoint union of any two non-isomorphic sun graphs $tvs(M_k \bigcup M_n)$.