منابع مشابه
Counting 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 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 کاملOn End-faithful Spanning Trees in Infinite Graphs
Let G be an infinite connected graph. A ray (from v) in G is a 1-way infinite path in G (with initial vertex v). An infinite connected subgraph of a ray R ⊂ G is called a tail of R. If X ⊂ G is finite, the infinite component of R\X will be called the tail of R in G\X. The following assertions are equivalent for rays P,Q ⊂ G: (i) There exists a ray R ⊂ G which meets each of P and Q infinitely of...
متن کاملOn spanning trees and k-connectedness in infinite graphs
If two rays P,Q ⊂ G satisfy (i)–(iii), we call them end-equivalent in G. An end of G is an equivalence class under this relation, and E(G) denotes the set of ends of G. For example, the 2-way infinite ladder has two ends, the infinite grid Z×Z and every infinite complete graph have one end, and the dyadic tree has 20 ends. This paper is concerned with the relationship between the ends of a conn...
متن کاملTopological paths, cycles and spanning trees in infinite graphs
We study topological versions of paths, cycles and spanning trees in infinite graphs with ends that allow more comprehensive generalizations of finite results than their standard notions. For some graphs it turns out that best results are obtained not for the standard space consisting of the graph and all its ends, but for one where only its topological ends are added as new points, while rays ...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1991
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1991.102432