Let X be a regular graph with degree k ≥ 3 and order n. Then the number of spanning trees of X is κ ( X ) < γ κ c k n exp ( − ∑ i = 3 n k / 2 ( 1 − 2 i k n ) p i β i , k ( 1 / k ) ) , where γk, ck and βi,k(1/k) are positive constants, and pi is the number of equivalence classes of certain closed walks of length i in X.
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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 ...
Let C(G) denote the number of spanning trees of a graph G . It is shown that there is a function ~ ( k ) that tends to zero as k tends to infinity such that ...
Dec 12, 2011 · For any graph G, the number of spanning trees τ(G) of G is equal to τ(G−e)+τ(G/e), where e is any edge of G, and where G−e is the deletion of e ...
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Note that the number of possible resulting oriented subgraphs H is d(G). Every spanning tree T of G will be represented among these H exactly n - 1 times (with ...
Sep 26, 2013 · We give an asympotic formula for the expected number of spanning trees in a uniformly random d-regular graph with n vertices.
In this paper we investigate the number of spanning trees of a regular graph. We succeed in finding a tight upper bound in terms of the numbers of small ...
In this paper, we study the number of spanning forests of regular graphs. Let and denote the number of spanning trees and spanning forests, respectively.
Jul 13, 2024 · If a graph is a complete graph with n vertices, then total number of spanning trees is n(n-2) where n is the number of nodes in the graph.
Sep 25, 2013 · We give an asympotic formula for the expected number of spanning trees in a uniformly random d-regular graph with n vertices. (The asymptotics ...