Enumeration of Regular Graph Coverings Having Finite Abelian Covering Transformation Groups

1998 ◽  
Vol 11 (2) ◽  
pp. 273-285 ◽  
Author(s):  
Jin Ho Kwak ◽  
Jang-Ho Chun ◽  
Jaeun Lee
Keyword(s):  
Regular Graph ◽  
Transformation Groups ◽  
Abelian Covering ◽  
Graph Coverings

Graph Coverings and (Im)primitive Homology: Examples of Low Degree

2021 ◽  
pp. 1-8
Author(s):  
Destine Lee ◽  
Iris Rosenblum-Sellers ◽  
Jakwanul Safin ◽  
Anda Tenie
Keyword(s):  
Low Degree ◽  
Graph Coverings

scholarly journals Critical group structure from the parameters of a strongly regular graph

2021 ◽  
Vol 180 ◽  
pp. 105424
Author(s):  
Joshua E. Ducey ◽  
David L. Duncan ◽  
Wesley J. Engelbrecht ◽  
Jawahar V. Madan ◽  
Eric Piato ◽  
...  
Keyword(s):  
Regular Graph ◽  
Group Structure ◽  
Strongly Regular Graph ◽  
Critical Group ◽  
Strongly Regular

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).

ON THE REGULAR GRAPH RELATED TO THE G-CONJUGACY CLASSES

2021 ◽  
pp. 1-5
Author(s):  
SH. RAHIMI ◽  
Z. AKHLAGHI
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Conjugacy Class ◽  
Regular Graph ◽  
Simple Graph ◽  
Conjugacy Classes ◽  
A Finite Group

Abstract Given a finite group G with a normal subgroup N, the simple graph $\Gamma _{\textit {G}}( \textit {N} )$ is a graph whose vertices are of the form $|x^G|$ , where $x\in {N\setminus {Z(G)}}$ and $x^G$ is the G-conjugacy class of N containing the element x. Two vertices $|x^G|$ and $|y^G|$ are adjacent if they are not coprime. We prove that, if $\Gamma _G(N)$ is a connected incomplete regular graph, then $N= P \times {A}$ where P is a p-group, for some prime p, $A\leq {Z(G)}$ and $\textbf {Z}(N)\not = N\cap \textbf {Z}(G)$ .

scholarly journals F-Expansive transformation groups

1979 ◽  
Vol 10 (1) ◽  
pp. 67-85 ◽  
Author(s):  
H.B. Keynes ◽  
M. Sears
Keyword(s):  
Transformation Groups

scholarly journals Isomorphisms and automorphisms of graph coverings

1991 ◽  
Vol 98 (3) ◽  
pp. 175-183 ◽  
Author(s):  
M. Hofmeister
Keyword(s):  
Graph Coverings
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