Normalized Laplacian spectra of central vertex join and central edge join of graphs

TL;DR

This paper computes the normalized Laplacian spectra of central graphs, vertex joins, and edge joins of regular graphs, and also determines their Kemeny's constant and degree Kirchhoff index, advancing spectral graph theory understanding.

Contribution

It introduces formulas for normalized Laplacian spectra and related indices for central graph operations on regular graphs, providing new spectral analysis tools.

Findings

Derived spectra formulas for central graphs and joins of regular graphs.

Calculated Kemeny's constant and Kirchhoff index for these graph operations.

Enhanced understanding of spectral properties in graph theory.

Abstract

In this paper, we compute normalized Laplacian spectra of central graph of a regular graph, central vertex join and central edge join of two regular graphs. Also, we determine their Kemeny's constant and degree Kirchhoff index.