Identities for minors of the Laplacian, resistance and distance matrices

DOI10.1016/j.laa.2011.03.028zbMath1221.05227OpenAlexW2086540021MaRDI QIDQ551303

Sivaramakrishnan Sivasubramanian, Ravindra B. Bapat

Publication date: 15 July 2011

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2011.03.028

zbMATH Keywords

determinantLaplacian\(q\)-analoguedistance matrixresistance matrixpartitioned matrix

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Determinants, permanents, traces, other special matrix functions (15A15) Matrix equations and identities (15A24) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items

Resistance matrices of balanced directed graphs, On a quadratic programming problem involving distances in trees, Algorithmic techniques for finding resistance distances on structured graphs, Hitting time quasi-metric and its forest representation, On solving a non-convex quadratic programming problem involving resistance distances in graphs, Color signless Laplacian energy of graphs, Some results on the Laplacian spectra of graphs with pockets, Simple expressions for the long walk distance, The walk distances in graphs, A recursion formula for resistance distances and its applications, Identities for minors of the Laplacian, resistance and distance matrices of graphs with arbitrary weights, The Arithmetic Tutte polynomial of two matrices associated to Trees, The 2-Steiner distance matrix of a tree, A \(q\)-analogue of the bipartite distance matrix of a nonsingular tree, On the resistance matrix of a graph

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(q\)-analogs of distance matrices of 3-hypertrees
• Zeta functions of line, middle, total graphs of a graph and their coverings
• Distance matrix polynomials of trees
• A note on the zeta function of a graph
• Zeta functions of finite graphs and coverings
• A \(q\)-analogue of the distance matrix of a tree
• Matrix Analysis
• Generalized matrix tree theorem for mixed graphs
• A Combinatorial Proof of the All Minors Matrix Tree Theorem
• On the distance matrix of a directed graph
• THE IHARA-SELBERG ZETA FUNCTION OF A TREE LATTICE
• On the Addressing Problem for Loop Switching