article · Creative Mathematics and Informatics · 2025

On the Eigenvalues of Hamming Matrix and Hamming Energy of a Graph

Harishchandra S. Ramane, Thippeswamy Shivaprasad, Sheena Y. Chowri

Cited by 1Open access

Abstract

Let G be a graph with n vertices and m edges. Let V(G) = {v1,v2,...,vn} be the vertex set of G. Thestring s(vi) is the row in the incidence matrix of G corresponding to the vertex vi, which is an m-tuple in Zm 2 . The Hamming matrix H(G) = [hij] of a graph G is an n×nmatrix, whose (i,j)-th entry is the Hamming distance between the strings s(vi) and s(vj). The Hamming energy HE(G) of a graph G is the sum of the absolute values of the eigenvalues of H(G). Recently the Hamming energy is introduced and obtained bounds for it in terms of the Hammingindexandobservedits predictive potentiality by correlating the physicochemical properties of molecules. In this paper we give the better bound for Hamming energy in terms of number of vertices and edges. Also obtain the largest eigenvalue of the Hamming matrix of a regular graph. Further obtain explicitly the eigenvalues of the Hamming matrix and Hamming energy of a complete bipartite graph

Cite this paper

APA 7

Ramane, H. S., Shivaprasad, T., & Chowri, S. Y. (2025). On the Eigenvalues of Hamming Matrix and Hamming Energy of a Graph. Creative Mathematics and Informatics, 34(2), 291–298. https://doi.org/10.37193/cmi.2025.02.11

MLA 9

Ramane, Harishchandra S., et al. “On the Eigenvalues of Hamming Matrix and Hamming Energy of a Graph.” Creative Mathematics and Informatics, vol. 34, no. 2, 2025, pp. 291–98, https://doi.org/10.37193/cmi.2025.02.11.

Chicago

Ramane, Harishchandra S., Thippeswamy Shivaprasad, and Sheena Y. Chowri. 2025. “On the Eigenvalues of Hamming Matrix and Hamming Energy of a Graph.” Creative Mathematics and Informatics 34 (2): 291–98. https://doi.org/10.37193/cmi.2025.02.11.

Harvard

Ramane, H.S., Shivaprasad, T. and Chowri, S.Y. (2025) ‘On the Eigenvalues of Hamming Matrix and Hamming Energy of a Graph’, Creative Mathematics and Informatics, 34(2), pp. 291–298. Available at: https://doi.org/10.37193/cmi.2025.02.11.

BibTeX

@article{ramane2025eigenvalues,
  title = {{On the Eigenvalues of Hamming Matrix and Hamming Energy of a Graph}},
  author = {Ramane, Harishchandra S. and Shivaprasad, Thippeswamy and Chowri, Sheena Y.},
  journal = {Creative Mathematics and Informatics},
  volume = {34},
  number = {2},
  pages = {291--298},
  year = {2025},
  doi = {10.37193/cmi.2025.02.11}
}

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