In this article, we give short proofs for the formulas without using zeta functions. Furthermore, by applying the formula that enumerates the number of spanning trees in the line graph of an (r, s)‐semiregular graph, we give a new proof of Cayley's Theorem. 2013 Wiley Periodicals, Inc...
The relative importance of two groups of nodes in the graph can be compared with respect to the number of spanning trees. 通过比较生成树的数目,可以判断图中任意数目的两组节点的相对重要性。 www.magsci.org 3. There is a recursive formula for the number of spanning trees in a graph. 对于一...
The number of spanning trees of composite graphs. 来自 国家科技图书文献中心 喜欢 0 阅读量: 11 作者: J Li,WC Shiu 摘要: Summary: Some formulae for computing the numbers of spanning trees of the corona and the join of graphs are deduced. 关键词: Spanning trees Laplacian spectrum Matrix-...
The formula... A Miola - 《Information Processing Letters》 被引量: 26发表: 1984年 Graph Theoretical Means for Calculating Kekule and Hueckel Parameters in Benzenoid and Related Systems In 1990, Kh. Al-Khnaifes, P. John and the author described some simple algorithms for calculating certain ...
Based on the matrix form of Kirchhoff's theorem about the number of spanning trees of a graph three new formulae are derived for enumerating the bases of a transportation problem with prohibitions. These formulae are derived in the case where the set of prohibitions is of a special type. ...
GraphTheory CliqueNumber compute clique number of graph MaximumClique find maximum clique in graph Calling Sequence Parameters Options Description Examples References Compatibility Calling Sequence CliqueNumber( G ) CliqueNumber( G , opt ) MaximumClique(
A cycle on m vertices is denoted Cm. The complement of a graph G is denoted G¯. For any graph G, let c(G) denote the number of cycles in G. The number e is the base of the natural logarithm. The Stirling’s approximation formula says that as n→∞, (1)n!=(1+o(1))2π...
Expression for the Number of Spanning Trees of Line Graphs of Arbitrary Connected Graphs For any graph G, let t(G) be the number of spanning trees of G, L(G) be the line graph of G, and for any nonnegative integer r, Sr(G) be the graph\nobtaine... Fengming,Dong,Weigen,......
Defining the transition from benign to malignant tissue is fundamental to improving early diagnosis of cancer1. Here we use a systematic approach to study spatial genome integrity in situ and describe previously unidentified clonal relationships. We used
Based on the history that the Emperor Constantine decreed that any undefended place (with no legions) of the Roman Empire must be protected by a “stronger” neighbor place (having two legions), a graph theoretical model called Roman domination in graphs was described. A Roman dominating functio...