منابع مشابه
Perfect Matchings in Edge-Transitive Graphs
We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...
متن کاملCovering graphs with matchings of fixed size
Let m be a positive integer and let G be a graph. We consider the question: can the edge set E(G) of G be expressed as the union of a set M of matchings of G each of which has size exactly m? If this happens, we say that G is [m]-coverable and we call M an [m]-covering of G. It is interesting (and probably of some practical value) to consider minimum [m]-coverings, i.e. [m]-coverings containing...
متن کاملGraphs with maximal induced matchings of the same size
A graph is well-indumatched if all its maximal induced matchings are of the same size. We first prove that recognizing the class WIM of well-indumatched graphs is a co-NPcomplete problem even for (2P5,K1,5)-free graphs. We then show that the well-known decision problems such as Independent Dominating Set, Independent Set, and Dominating Set are NP-complete for well-indumatched graphs. We also s...
متن کاملCovering cubic graphs with matchings of large size
Let m be a positive integer and let G be a cubic graph of order 2n. We consider the problem of covering the edge-set of G with the minimum number of matchings of size m. This number is called the excessive [m]-index of G in the literature. The case m = n, that is, a covering with perfect matchings, is known to be strictly related to an outstanding conjecture of Berge and Fulkerson. In this pape...
متن کاملAverage Degree-Eccentricity Energy of Graphs
The concept of average degree-eccentricity matrix ADE(G) of a connected graph $G$ is introduced. Some coefficients of the characteristic polynomial of ADE(G) are obtained, as well as a bound for the eigenvalues of ADE(G). We also introduce the average degree-eccentricity graph energy and establish bounds for it.
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2020
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-020-02136-1