A study on k-coalescence of two graphs
Abstract
The k-coalescence of two graphs is obtained by merging a k-clique of each graph. The Aα-matrix of a graph is the convex combination of its degree matrix and adjacency matrix. In this paper, we present some structural properties of a non-regular graph which is obtained from the k-coalescence of two graphs. Also, we derive the Aα-characteristic poly- nomial of k-coalescence of two graphs and then compute the Aα-spectra of k-coalescence of two complete graphs. In addition, we estimate the Aα-energy of k-coalescence of two complete graphs. Furthermore, we obtain some topological indices of vertex coalescence of two graphs, and as an application, we determine the Wiener, hyper-Wiener and Zagreb indices of Lollipop and Dumbbell graphs.
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