Classifying pentavalnet symmetric graphs of order $24p$
author
Abstract:
A graph is said to be symmetric if its automorphism group is transitive on its arcs. A complete classification is given of pentavalent symmetric graphs of order 24p for each prime p. It is shown that a connected pentavalent symmetric graph of order 24p exists if and only if p=2, 3, 5, 11 or 17, and up to isomorphism, there are only eleven such graphs.
similar resources
Classifying cubic symmetric graphs of order 8p or 8p2
A graph is s-regular if its automorphism group acts regularly on the set of its s-arcs. In this paper, we classify the s-regular elementary Abelian coverings of the three-dimensional hypercube for each s ≥ 1 whose fibre-preserving automorphism subgroups act arc-transitively. This gives a new infinite family of cubic 1-regular graphs, in which the smallest one has order 19 208. As an application...
full textClassifying a Family of Symmetric Graphs
Let Γ be a G-symmetric graph admitting a nontrivial G-invariant partition B of block size v. For blocks B,C of B adjacent in the quotient graph ΓB, let k be the number of vertices in B adjacent to at least one vertex in C. In this paper we classify all possibilities for (Γ,ΓB, G) in the case where k = v − 1 ≥ 2 and B(α) = B(β) for adjacent vertices α, β of Γ, where for a vertex of Γ, say γ ∈ B,...
full textPentavalent symmetric graphs of order 2pq
A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, a complete classification of connected pentavalent symmetric graphs of order 12p is given for each prime p. As a result, a connected pentavalent symmetric graph of order 12p exists if and only if p = 2, 3, 5 or 11, and up to isomorphism, there are only nine such graphs: one for each p = 2, 3 ...
full textTETRAVALENT SYMMETRIC GRAPHS OF ORDER 9p
A graph is symmetric if its automorphism group acts transitively on the set of arcs of the graph. In this paper, we classify tetravalent symmetric graphs of order 9p for each prime p.
full textHEPTAVALENT SYMMETRIC GRAPHS OF ORDER 6p
A graph is symmetric if its automorphism group acts transitively on the set of arcs of the graph. In this paper, we classify connected heptavalent symmetric graphs of order 6p for each prime p. As a result, there are three sporadic such graphs: one for p = 5 and two for p = 13.
full textTHE ORDER GRAPHS OF GROUPS
Let $G$ be a group. The order graph of $G$ is the (undirected)graph $Gamma(G)$,those whose vertices are non-trivial subgroups of $G$ and two distinctvertices $H$ and $K$ are adjacent if and only if either$o(H)|o(K)$ or $o(K)|o(H)$. In this paper, we investigate theinterplay between the group-theoretic properties of $G$ and thegraph-theoretic properties of $Gamma(G)$. For a finite group$G$, we s...
full textMy Resources
Journal title
volume 43 issue 6
pages 1855- 1866
publication date 2017-11-30
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023