The number of spanning trees of a family of 2-separable weighted graphs

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 spec...

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Veröffentlicht in:	Discrete Applied Mathematics 2017-10, Vol.229, p.154-160
Hauptverfasser:	Gong, Helin, Li, Shuli
Format:	Artikel
Sprache:	eng
Schlagworte:	2-separable Electrically equivalent Graph theory Graphs Spanning tree Studies Trees Weighted graph
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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.
doi_str_mv	10.1016/j.dam.2017.05.003
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source	Elsevier ScienceDirect Journals Complete; EZB-FREE-00999 freely available EZB journals
subjects	2-separable Electrically equivalent Graph theory Graphs Spanning tree Studies Trees Weighted graph
title	The number of spanning trees of a family of 2-separable weighted graphs
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