An efficient approach for counting the number of spanning trees in circulant and related graphs
نویسندگان
چکیده
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 کاملCounting Spanning Trees and Other Structures in Non-constant-jump Circulant Graphs
Circulant graphs are an extremely well-studied subclass of regular graphs, partially because they model many practical computer network topologies. It has long been known that the number of spanning trees in n-node circulant graphs with constant jumps satisfies a recurrence relation in n. For the non-constant-jump case, i.e., where some jump sizes can be functions of the graph size, only a few ...
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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 کاملFurther analysis of the number of spanning trees in circulant graphs
Let 1 s1<s2< · · ·<sk n/2 be given integers. An undirected even-valent circulant graph, C12k n , has n vertices 0, 1, 2, . . ., n− 1, and for each si (1 i k) and j (0 j n− 1) there is an edge between j and j + si (mod n). Let T (C12k n ) stand for the number of spanning trees of C12k n . For this special class of graphs, a general and most recent result, which is obtained in [Y.P. Zhang, X.Yong...
متن کاملA formula for the number of spanning trees in circulant graphs with non-fixed generators∗
We consider the number of spanning trees in circulant graphs of βn vertices with generators depending linearly on n. The matrix tree theorem gives a closed formula of βn factors; while we derive a formula of β−1 factors. The spanning tree entropy of these graphs is then compared to the one of fixed generated circulant graphs.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 310 شماره
صفحات -
تاریخ انتشار 2010