On the Chromatic Uniqueness of Edge-Gluing of Complete Bipartite Graphs and Cycles

In this paper, we give an alternative proof for the fact that the graph obtained by overlapping the cycle \(C_m\) (\(m \geq 3\)) and the complete bipartite graph \(K_{2,s}\) (\(s \geq 1\)) at an edge is uniquely determined by its chromatic polynomial. This result provides a partial solution to a question raised in [7].