Year: 2026
Type: article
Abstract: The Hamming distance between two strings of the same length is the count of positions at which their corresponding symbols are different.For a graph G of order n, the Hamming matrix is H(G) = [hij]n×n, where hij equals the Hamming distance between s(vi) and s(vj), and hii = 0; here, s(vi) represents the string corresponding to the i-th row of the incidence matrix of G.The Hamming energy was recently introduced in analogy with adjacency energy.In this paper, it is shown that, except for edgeless graphs and K2, the Hamming matrix has exactly one positive eigenvalue; as a result, a general expression for the Hamming energy is derived.This result shows that the study of the Hamming energy reduces to the analysis of the largest eigenvalue of the Hamming matrix.These results extend several earlier findings on the Hamming matrix in the literature.
Source: Discrete Mathematics Letters
Institutions: Karnatak University, Government of Karnataka
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7223553412