A regular and edge-transitive graph that is not vertex-transitive is said to be semisymmetric. Every semisymmetric graph is necessarily bipartite, with the two parts having equal size and the automorphism group acting transitively on each of these two parts. A semisymmetric graph is called biprimiti
Note on Infinite Families of Trivalent Semisymmetric Graphs
โ Scribed by Seymour Lipschutz; Ming-Yao Xu
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 60 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
โฆ Synopsis
A simple undirected graph is said to be semisymmetric if it is regular and edge-transitive but not vertex-transitive. This paper uses the groups PSL(2, p) and PGL(2, p), where p is a prime, to construct two new infinite families of trivalent semisymmetric graphs.
๐ SIMILAR VOLUMES
We present a construction of two infinite graphs \(G_{1}, G_{2}\) and of an infinite set of graphs such that \(\mathscr{F}\) is an antichain with respect to the minor relation and, for every graph \(G\) in \(\mathscr{F}\), both \(G_{1}\) and \(G_{2}\) are subgraphs of \(G\) but no graph obtained fro
## Abstract In this paper, it is proven that for each __k__ โฅ 2, __m__ โฅ 2, the graph ฮ~__k__~(__m,โฆ,m__), which consists of __k__ disjoint paths of length __m__ with same ends is chromatically unique, and that for each __m, n__, 2 โค __m__ โค __n__, the complete bipartite graph __K__~__m,n__~ is chr
## Abstract Let __G__ be a 4โregular planar graph and suppose that __G__ has a cycle decomposition __S__ (i.e., each edge of __G__ is in exactly one cycle of the decomposition) with every pair of adjacent edges on a face always in different cycles of __S__. Such graphs, called GrรถtzschโSachs graphs
Let Do0 be the fundamental discriminant of an imaginary quadratic field, and hรฐDร its class number. In this paper, we show that for any prime p > 3 and e ยผ ร1; 0; or 1, ] รX oDo0 j hรฐDรc0 รฐmod pร and D p ยผ e 4 p ffiffiffiffi X p log X :
## Abstract The existence of an infinite graph which is not isomorphic to a proper minor of itself was proved by Oporowski. In the present note, it is shown that an analogous result holds when immersions are considered instead of minors. The question whether or not the same is true for weak immersi