A natural generalization of a regular (or equitable) partition of a graph, which makes sense also for non-regular graphs, is the so-called weight-regular partition, which gives to each vertex u ∈ V a weight that equals the corresponding entry ν u of the Perron eigenvector ν . This ...
Twitter Google Share on Facebook regular graph Wikipedia regular graph [′reg·gə·lər ¦graf] (mathematics) A graph whose vertices all have the same degree. McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc. ...
In this paper we show that there exists a one-regular cubic graph of order 2 p or 2 p 2 where p is a prime if and only if 3 is a divisor of p – 1 and the graph has order greater than 25. All of those one-regular cubic graphs are Cayley graphs on dihedral groups and there...
Derving Bipartite graphs from hypergraphs Proposition 1 Any regular uniform hypergraph HGk,d can be represented usefully by a bipartite graph BGn,m: the vertices V and the edges E of the hypergraph are the partitions of BG, and (v i , e j ) are connected with an edge if and only if ...
On strongly regular self - complementary graphs It is shown that certain conditions assumed on a regular self-complementary graph are not sufficient for the graph to be strongly regular, answering in the... Sergio,Ruiz - 《Journal of Graph Theory》 被引量: 8发表: 1981年 Partitions of sets ...
Internal Partitions of Regular Graphs An internal partition of an n -vertex graph is a partition of V such that every vertex has at least as many neighbors in its own part as in the other part... A Ban,N Linial - 《Journal of Graph Theory》 被引量: 13发表: 2016年 Complexity...
Bounds for Judicious Balanced Bipartitions of Graphs A bipartition of the vertex set of a graph is called balanced if the sizes of the sets in the bipartition differ by at most one. Bollob ' as and Scott prov... YRH Cao - 《Graphs & Combinatorics》 被引量: 0发表: 2018年 Balanced Judi...
Numerical Estimation of the Asymptotic Behaviour of Solid Partitions of an Integer The number of solid partitions of a positive integer is an unsolved problemin combinatorial number theory. In this paper, solid partitions are studiednumer... V Mustonen,R Rajesh - 《Journal of Physics A General Ph...
3.1. Solution Graphs: Pattern Matching via Reachability We take a slightly unorthodox view of regular expressions in this section. This viewpoint will make it easier to precompute solutions to small regular expression queries and then merge them with other solutions to answer the query. Essentially,...
arXiv:1706.05460v1 [math.CO] 17 Jun 2017STRONGLY REGULAR CAYLEY GRAPHS FROM PARTITIONS OFSUBDIFFERENCE SETS OF THE SINGER DIFFERENCE SETSKOJI MOMIHARA ∗ , QING XIANG †Abstract. In this paper, we give a new lifting construction of “hyperbolic” type of strongly regularCayley graphs. Also ...