2014•Hu'nan Shifan Daxue xuebao. Ziran kexue banRequires access

Inverse of Adjacency Matrix of a Graph with Matrix Weights

Cui Deng-la

Abstract

The weighted graphs that the edge weights are square matrices with fixed orders are considered.The adjacency and skew-adjacency matrix of a weighted graph is defined in a natural way.The formula is obtained for the inverses of the adjacency and skew-adjacency matrices of a weighted graph when its underlying graph is a bipartite graph with a unique perfect matching,and some applications are given in inverse of block matrices.

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Key concepts: Adjacency matrix, Graph energy, Combinatorics, Mathematics, Adjacency list, Bipartite graph, Degree matrix, Discrete mathematics