On the Net Distance Matrix of a Signed Block Graph

Authors

  • Zixuan Hong MOE-LCSM, CHP-LCOCS, School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P. R. China
  • Yaoping Hou MOE-LCSM, CHP-LCOCS, School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P. R. China

DOI:

https://doi.org/10.37256/cm.4120232065

Keywords:

signed block graph, net distance matrix, net Laplacian matrix, adjacency matrix, Moore-Penrose inverse

Abstract

A connected signed graph Ġ, where all blocks of it are positive cliques or negative cliques (of possibly varying sizes), is called a signed block graph. Let A, N and D̃ be adjacency, net Laplacian and net distance matrices of a signed block graph, respectively. In this paper the formulas for the determinant of A and D̃ were given firstly. Then the inverse (resp. Moore-Penrose inverse) of D̃ is obtained if it is nonsingular (resp. singular), which is the sum of a Laplacian-like matrix and at most two matrices with rank 1.

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Published

2023-03-20

Issue

Contemporary Mathematics, Volume 4 Issue 1 (2023), 1-181

Section

Research Article

How to Cite

1.
On the Net Distance Matrix of a Signed Block Graph. Contemp. Math. [Internet]. 2023 Mar. 20 [cited 2025 Dec. 24];4(1):167-81. Available from: https://ojs353.mebyme.cn/index.php/CM/article/view/2065