Name
Abstract | ||
|---|---|---|
A connected symmetric graph of prime valency is basic if its automorphism group contains no nontrivial normal subgroup having more than two orbits. Let p be a prime and n a positive integer. In this paper, we investigate properties of connected pentavalent symmetric graphs of order 2 p n , and it is shown that a connected pentavalent symmetric graph of order 2 p n is basic if and only if it is either a graph of order 6 , 16 , 250 , or a graph of three infinite families of Cayley graphs on generalized dihedral groups-one family has order 2 p with p = 5 or 5 ź ( p - 1 ) , one family has order 2 p 2 with 5 ź ( p ź 1 ) , and the other family has order 2 p 4 . Furthermore, the automorphism groups of these basic graphs are computed. Similar works on cubic and tetravalent symmetric graphs of order 2 p n have been done.It is shown that basic graphs of connected pentavalent symmetric graphs of order 2 p n are symmetric elementary abelian covers of the dipole Dip 5 , and with covering techniques, uniqueness and automorphism groups of these basic graphs are determined. Moreover, symmetric Z p n -covers of the dipole Dip 5 are classified. As a byproduct, connected pentavalent symmetric graphs of order 2 p 2 are classified. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1016/j.disc.2016.05.008 | Discrete Mathematics |
Keywords | Field | DocType |
Symmetric graph,Cayley graph,Regular covering,Normal cover | Discrete mathematics,Odd graph,Comparability graph,Combinatorics,Indifference graph,Vertex-transitive graph,Chordal graph,Symmetric graph,1-planar graph,Mathematics,Pancyclic graph | Journal |
Volume | Issue | ISSN |
339 | 11 | 0012-365X |
Citations | PageRank | References |
1 | 0.37 | 16 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yan-quan Feng | 1 | 350 | 41.80 |
| Jin-Xin Zhou | 2 | 156 | 25.22 |
| Yan-Tao Li | 3 | 1 | 0.71 |