scholarly journals End-regular and End-orthodox generalized lexicographic products of bipartite graphs

2016 ◽  
Vol 14 (1) ◽  
pp. 229-236 ◽  
Author(s):  
Rui Gu ◽  
Hailong Hou
Keyword(s):  
Orthodox Semigroup ◽  
Bipartite Graphs ◽  
Endomorphism Monoid

AbstractA graph X is said to be End-regular (End-orthodox) if its endomorphism monoid End(X) is a regular (orthodox) semigroup. In this paper, we determine the End-regular and the End-orthodox generalized lexicographic products of bipartite graphs.

scholarly journals End-Completely-Regular and End-Inverse Lexicographic Products of Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Hailong Hou ◽  
Rui Gu
Keyword(s):  
Bipartite Graphs ◽  
Endomorphism Monoid ◽  
Regular Graphs ◽  
Completely Regular

A graphXis said to be End-completely-regular (resp., End-inverse) if its endomorphism monoid End(X) is completely regular (resp., inverse). In this paper, we will show that ifX[Y] is End-completely-regular (resp., End-inverse), then bothXandYare End-completely-regular (resp., End-inverse). We give several approaches to construct new End-completely-regular graphs by means of the lexicographic products of two graphs with certain conditions. In particular, we determine the End-completely-regular and End-inverse lexicographic products of bipartite graphs.

Bipartite Graphs and their Applications

1998 ◽  
Author(s):  
Armen S. Asratian ◽  
Tristan M. J. Denley ◽  
Roland Häggkvist
Keyword(s):  
Bipartite Graphs

Hurricane in Bipartite Graphs: The Lethal Nodes of Butterflies

2020 ◽  
Author(s):  
Qiuyu Zhu ◽  
Jiahong Zheng ◽  
Hao Yang ◽  
Chen Chen ◽  
Xiaoyang Wang ◽  
...  
Keyword(s):  
Bipartite Graphs

Trivalent Non-symmetric Vertex-Transitive Graphs of Order at Most 150

2008 ◽  
Vol 15 (03) ◽  
pp. 379-390 ◽  
Author(s):  
Xuesong Ma ◽  
Ruji Wang
Keyword(s):  
Automorphism Group ◽  
Bipartite Graphs ◽  
Type Ii ◽  
Symmetric Graph ◽  
Trivalent Graph ◽  
Block Graphs ◽  
Group A ◽  
Vertex Transitive ◽  
Vertex Transitive Graphs ◽  
Transitive Graphs

Let X be a simple undirected connected trivalent graph. Then X is said to be a trivalent non-symmetric graph of type (II) if its automorphism group A = Aut (X) acts transitively on the vertices and the vertex-stabilizer Av of any vertex v has two orbits on the neighborhood of v. In this paper, such graphs of order at most 150 with the basic cycles of prime length are investigated, and a classification is given for such graphs which are non-Cayley graphs, whose block graphs induced by the basic cycles are non-bipartite graphs.

scholarly journals Cycle partitions of regular graphs

2020 ◽  
pp. 1-24
Author(s):  
Vytautas Gruslys ◽  
Shoham Letzter
Keyword(s):  
Regular Graph ◽  
Bipartite Graphs ◽  
Disjoint Paths ◽  
Regular Graphs ◽  
Simple Construction ◽  
Vertex Set ◽  
Almost All ◽  
Vertex Disjoint

Abstract Magnant and Martin conjectured that the vertex set of any d-regular graph G on n vertices can be partitioned into $n / (d+1)$ paths (there exists a simple construction showing that this bound would be best possible). We prove this conjecture when $d = \Omega(n)$ , improving a result of Han, who showed that in this range almost all vertices of G can be covered by $n / (d+1) + 1$ vertex-disjoint paths. In fact our proof gives a partition of V(G) into cycles. We also show that, if $d = \Omega(n)$ and G is bipartite, then V(G) can be partitioned into n/(2d) paths (this bound is tight for bipartite graphs).

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