A formula for all minors of the adjacency matrix and an application

• Autorzy: R. B. Bapat , A. K. Lal , S. Pati
• Języki publikacji: EN

Abstrakty

EN

We supply a combinatorial description of any minor of the adjacency matrix of a graph. This description is then used to give a formula for the determinant and inverse of the adjacency matrix, A(G), of a graph G, whenever A(G) is invertible, where G is formed by replacing the edges of a tree by path bundles.

Słowa kluczowe

EN

Adjacency Matrix; Linear Subgraphs; Minors; Path Bundle

Kategorie tematyczne

• 05C05: Trees
• 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)
• 15A18: Eigenvalues, singular values, and eigenvectors

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2014
• Tom: 2
• Numer: 1

Daty

otrzymano

2014-01-25

zaakceptowano

2014-05-07

online

2014-06-09

Twórcy

autor

R. B. Bapat

• Stat-Math Unit, Indian Statistical Institute Delhi, 7-SJSS Marg, New Delhi, India

autor

A. K. Lal

autor

S. Pati

Bibliografia

• [1] R. B. Bapat. Graphs and Matrices. Hindustan Book Agency, New Delhi, (Copublished by Springer, London) 2011.
• [2] J. A. Bondy and U. S. R. Murty. Graph Theory with Applications. The Macmillan Press Ltd., London, 1976.
• [3] S. Chaiken. A Combinatorial Proof of the All Minors Matrix Tree Theorem. SIAM J alg disc meth, vol 3, no 3, 319–329, 1982.
• [4] D. M. Cvetkovic, M. Doob and H. Sachs. Spectra of Graphs. Academic Press, New York, 1979.
• [5] F. Harary. The Determinant of the Adjacency Matrix of a Graph. SIAM Review, vol 4, 202–210, 1962.
• [6] In-Jae Kim and B. L. Shader. Smith normal form and acyclic matrices. J Algebraic Combin, vol 29, no 1, 63–80, 2009.

Identyfikatory

DOI

10.2478/spma-2014-0009