Abstract

If positive weights are assigned to the edges of a graph $G$, then degree of a vertex is the sum of the weights of edges that are incident to the vertex. A graph with weighted edges is said to be irregular if the degrees of the vertices are distinct. The irregularity strength of a graph is the smallest $s$ such that the edges can be weighted with $\{1,2,3, \cdots, s\}$ and be irregular. This notion was defined by Chartrand et al. (G Chartrand, M. S. Jacobson, J. Lehel, O. R. Ollerman, S. Ruiz \&  Saba. 1988). In this paper, we discuss the irregularity strength of corona product of a graph with star graph $K_{1,n}$. We obtain a sufficient condition on the minimum degree of a graph $H$ which determines the irregularity strength of a graph $H$ having $p$ vertices with the star graph $K_{1,n}$.

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