New matrices for the spectral theory of mixed graphs, part II

G. Kalaivani1, R. Rajkumar1
1Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram — 624 302, Tamil Nadu, India

Abstract

The concept of the integrated adjacency matrix for mixed graphs was first introduced in [9], where its spectral properties were analyzed in relation to the structural characteristics of the mixed graph. Building upon this foundation, this paper introduces the integrated Laplacian matrix, the integrated signless Laplacian matrix, and the normalized integrated Laplacian matrix for mixed graphs. We further explore how the spectra of these matrices relate to the structural properties of the mixed graph.

Keywords: mixed graph, integrated Laplacian matrix, integrated signless Laplacian matrix, normalized integrated Laplacian matrix, spectrum