On the Net Distance Matrix of a Signed Block Graph

被引：0

作者：

Hong, Zixuan ^{[1
]}

Hou, Yaoping ^{[1
]}

机构：

[1] Hunan Normal Univ, Sch Math & Stat, CHP, MOE,LCSM,COCS, Changsha 410081, Hunan, Peoples R China

来源：

CONTEMPORARY MATHEMATICS | 2023年 / 4卷 / 01期

基金：

中国国家自然科学基金;

关键词：

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

D O I：

10.37256/cm.4120232065

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A connected signed graph G, 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 (D) over tilde 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 (D) over tilde were given firstly. Then the inverse (resp. Moore-Penrose inverse) of (D) over tilde 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.

引用

页码：167 / 181

页数：15

共 16 条

[1] Identities for minors of the Laplacian, resistance and distance matrices of graphs with arbitrary weights [J].

Ali, Patrick ;

Atik, Fouzul ;

Bapat, Ravindra B. .

LINEAR & MULTILINEAR ALGEBRA, 2020, 68 (02) :323-336

[2] An inverse formula for the distance matrix of a wheel graph with an even number of vertices [J].

Balaji, R. ;

Bapat, R. B. ;

Goel, Shivani .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2021, 610 :274-292

[3] On distance matrices and Laplacians [J].

Bapat, R ;

Kirkland, SJ ;

Neumann, M .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 401 :193-209

[4] On the adjacency matrix of a block graph [J].

Bapat, R. B. ;

Roy, Souvik .

LINEAR & MULTILINEAR ALGEBRA, 2014, 62 (03) :406-418

[5] Inverse of the distance matrix of a block graph [J].

Bapat, R. B. ;

Sivasubramanian, Sivaramakrishnan .

LINEAR & MULTILINEAR ALGEBRA, 2011, 59 (12) :1393-1397

[6]

Bapat R.B., 2018, GRAPHS MATRICES

[7] DISTANCE MATRIX POLYNOMIALS OF TREES [J].

GRAHAM, RL ;

LOVASZ, L .

ADVANCES IN MATHEMATICS, 1978, 29 (01) :60-88

[8] ADDRESSING PROBLEM FOR LOOP SWITCHING [J].

GRAHAM, RL ;

POLLAK, HO .

BELL SYSTEM TECHNICAL JOURNAL, 1971, 50 (08) :2495-+

[9]

Hosoya H., 1977, J. Graph Theory, V1, P85, DOI [10.1002/jgt.3190010116, DOI 10.1002/JGT.3190010116]

[10] Inverse of the distance matrix of a bi-block graph [J].

Hou, Yaoping ;

Sun, Yajing .

LINEAR & MULTILINEAR ALGEBRA, 2016, 64 (08) :1509-1517

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