The number of spanning trees of a family of 2-separable weighted graphs
Discrete Applied Mathematics, ISSN: 0166-218X, Vol: 229, Page: 154-160
2017
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Article Description
Based on electrically equivalent transformations on weighted graphs, in this paper, we present a formula for computing the number of spanning trees of a family of 2-separable graphs formed from two base graphs by 2-sum operations. As applications, we compute the number of spanning trees of some special 2-separable graphs. Then comparisons are made between the number of spanning trees and the number of acyclic orientations for this family of 2-separable graphs under certain constraints. We also show that a factorization formula exists for the sum of weights of spanning trees of a special splitting graph.
Bibliographic Details
http://www.sciencedirect.com/science/article/pii/S0166218X17302408; http://dx.doi.org/10.1016/j.dam.2017.05.003; http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85020450930&origin=inward; https://linkinghub.elsevier.com/retrieve/pii/S0166218X17302408; https://api.elsevier.com/content/article/PII:S0166218X17302408?httpAccept=text/xml; https://api.elsevier.com/content/article/PII:S0166218X17302408?httpAccept=text/plain; https://dul.usage.elsevier.com/doi/; https://dx.doi.org/10.1016/j.dam.2017.05.003
Elsevier BV
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