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The number of spanning trees in regular graphs
Author(s) -
Alon Noga
Publication year - 1990
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.3240010204
Subject(s) - combinatorics , mathematics , spanning tree , graph , simple graph , discrete mathematics
Let C ( G ) denote the number of spanning trees of a graph G . It is shown that there is a function ϵ( k ) that tends to zero as k tends to infinity such that for every connected, k ‐regular simple graph G on n vertices C ( G ) = { k [1 − δ( G )]} n . where 0 ≤ δ( G ) ≤ ϵ( k ).
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