منابع مشابه
Spanning trees and orientations of graphs
A conjecture of Merino and Welsh says that the number of spanning trees τ(G) of a loopless and bridgeless multigraph G is always less than or equal to either the number a(G) of acyclic orientations, or the number c(G) of totally cyclic orientations, that is, orientations in which every edge is in a directed cycle. We prove that τ(G) ≤ c(G) if G has at least 4n edges, and that τ(G) ≤ a(G) if G h...
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A spanning tree of graph G is a spanning subgraph of G that is a tree. In this paper, we focus our attention on (n,m) graphs, where m = n, n + 1, n + 2, n+3 and n + 4. We also determine some coefficients of the Laplacian characteristic polynomial of fullerene graphs.
متن کاملNUMBER OF SPANNING TREES FOR DIFFERENT PRODUCT GRAPHS
In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was n...
متن کاملcounting the number of spanning trees of graphs
a spanning tree of graph g is a spanning subgraph of g that is a tree. in this paper, we focusour attention on (n,m) graphs, where m = n, n + 1, n + 2 and n + 3. we also determine somecoefficients of the laplacian characteristic polynomial of fullerene graphs.
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Let k be an integer, k ≥ 3, and let Zk be the cyclic group of order k. Take λk ∈ [k+2,∞) to be the smallest integer such that for every λk-edge-connected graph G and every mapping f : V (G) → Zk with |E(G)| k ≡ ∑ v∈V (G) f(v), there exits an orientation for G such that for each vertex v, d G (v) k ≡ f(v), where d G (v) denotes the out-degree of v. Lovász, Thomassen, Wu, and Zhang (2013) proved ...
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ژورنال
عنوان ژورنال: Journal of Combinatorics
سال: 2010
ISSN: 2156-3527,2150-959X
DOI: 10.4310/joc.2010.v1.n2.a1