A novel algebraic technique for adjacency matrices of some derived graphs

Abstract

Graph energy has been the main concern of spectral graph theory in the last five decades. The classical graph energy is the sum of the absolute values of the eigenvalues of the adjacency matrix. In many research papers, different versions of graph energy by utilizing different graph matrices are introduced. For many graph types corresponding to molecular structures, the energy is determined. The theory is complete for complete bipartite graphs. For derived graphs, the problem was settled partially for line, total, double and subdivision graphs. In this paper, the more complex cases of power graphs, shadow, image and core graphs are discussed, and the adjacency matrices of these derived graph classes are formed in terms of very simple submatrices.

Keywords

• Adjacency matrix
• derived graph
• line graph
• 05C07, 05C10, 05C30, 68R10