Central vertex join and central edge join of two graphs

Abstract

The central graph $C(G)$ of a graph $G$ is obtained by sub dividing each edge of $G$ exactly once and joining all the nonadjacent vertices in $G$. In this paper, we compute the adjacency, Laplacian and signless Laplacian spectra of central graph of a connected regular graph. Also, we define central vertex join and central edge join of two graphs and calculate their adjacency spectrum, Laplacian spectrum and signless Laplacian spectrum. As an application, some new families of integral graphs and cospectral graphs are constructed. In addition to that the Kirchhoff index and number of spanning trees of the new joins are determined.

Keywords

• central graph
• adjacency spectrum
• laplacian spectrum
• central vertex join
• central edge join