Inverse of α-Hermitian Adjacency Matrix of a Unicyclic Bipartite Graph

被引：0

作者：

Alomari O. ^{[1
]}

Abudayah M. ^{[2
]}

AbuGhneim O. ^{[3
]}

机构：

[1] College of Engineering and Technology, American University of the Middle East

[2] School of Basic Sciences and Humanities, German Jordanian University, Madaba

[3] Department of Mathematics, Faculty of Science, The University of Jordan, Amman

来源：

Journal of Combinatorial Mathematics and Combinatorial Computing | 2024年 / 119卷

关键词：

Bipartite mixed graphs; Inverse matrix; Mixed graphs; Perfect matching; Unicyclic bipartite mixed graphs; α-Hermitian adjacency matrix;

D O I：

10.61091/jcmcc119-07

中图分类号：

学科分类号：

摘要：

Let X be bipartite mixed graph and for a unit complex number α, Hα be its α-hermitian adjacency matrix. If X has a unique perfect matching, then Hα has a hermitian inverse Hα−1. In this paper we give a full description of the entries of Hα−1 in terms of the paths between the vertices. Furthermore, for α equals the primitive third root of unity γ and for a unicyclic bipartite graph X with unique perfect matching, we characterize when Hγ−1 is ±1 diagonally similar to γ-hermitian adjacency matrix of a mixed graph. Through our work, we have provided a new construction for the ±1 diagonal matrix. © 2024 the Author(s), licensee Combinatorial Press.

引用

页码：63 / 73

页数：10

共 12 条

[1]

Jovanovic I.M., Non-negative spectrum of a digraph, Ars Math. Contemp, 12, 1, pp. 167-182, (2017)

[2]

Alomari O., Abudayah M., Sander T., The non-negative spectrum of a digraph, Open Mathematics, 18, 1, pp. 22-35, (2020)

[3]

Guo K., Mohar B., Hermitian adjacency matrix of digraphs and mixed graphs, Journal of Graph Theory, 85, 1, pp. 217-248, (2017)

[4]

Liu J., Li X., Hermitian-adjacency matrices and Hermitian energies of mixed graphs, Linear Algebra and its Applications, 466, pp. 182-207, (2015)

[5]

Mohar B., A new kind of Hermitian matrices for digraphs, Linear Algebra and its Applications, 584, pp. 343-352, (2020)

[6]

Deza M.M., Deza E., Deza M.M., Deza E., Distances in Physics and Chemistry, Encyclopedia of Distances, pp. 487-519, (2014)

[7]

Pavlikova S., Jediny J.K., On the inverse and the dual index of a tree, Linear and Multilinear Algebra, 28, 1-2, pp. 93-109, (1990)

[8]

McLeman C., McNicholas E., Graph invertibility, Graphs and Combinatorics, 30, pp. 977-1002, (2014)

[9]

Akbari S., Kirkland S.J., On unimodular graphs, Linear Algebra and its Applications, 421, 1, pp. 3-15, (2007)

[10]

Abudayah M., Alomari O., Sander T., Hermitian adjacency matrices of mixed graphs, (2021)

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