We study an edge irregular reflexive k-labelling for the generalized friendship graphs, also known as flowers (a symmetric collection of cycles meeting at a common vertex), and determine the exact value of the reflexive edge strength for several subfamilies of the generalized friendship graphs.

For a simple graph G with no isolated edges and at most, one isolated vertex, a labeling $\phi :E\left(G\right)\to \{1,2,\dots ,k\}$ of positive integers to the edges of G is called irregular if the weights of the vertices, defined as $w{t}_{\phi }\left(v\right)={\sum }_{u\in N\left(v\right)}\phi \left(uv\right)$, are all different. The irregularity strength of a graph G is known as the maximal integer k, minimized over all irregular labelings, and is set to ∞ if no such labeling exists. In this paper, we determine the exact value of the irregularity strength and the modular irregularity strength of fan graphs.

Discussiones Mathematicae Graph Theory