2024/01/27 by Shivani Tushar Parab, Parab, Shivani Tushar, Raisa DSouza +1
Computer Science · Mathematics · #05C50 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2401.15300
openalex publication_date 2024/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we present two new matrices, namely the resistance Laplacian and resistance signless Laplacian matrix of a connected graph. We provide a generalized form of these matrices for different classes of graphs, including the complete graph, complete bipartite graph, and cycle. We investigate the spectral properties of these matrices, analyzing their eigenvalues and eigenvectors. Moreover, we introduce a concept similar to graph energy and define it as the resistance Laplacian energy of a graph and further discuss some bounds for this energy.