The P 3 -graph of a finite simple graph G is the graph whose vertices are the 3-vertex paths of G, with adjacency between two such paths whenever their union is a 4-vertex path or a 3-cycle. In this paper we show that connected finite simple graphs G and H with isomorphic P 3 -graphs are either isom
Isomorphisms ofP3-graphs
β Scribed by Li, Xueliang
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 324 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
For graphs G and G' with minimum degree at least 3 and satisfying one of three other conditions, w e prove that any isomorphism from the &graph P3(G) onto P3(G') can be induced by a (vertex-) isomorphism of G onto G'. This in some sense can be viewed as a counterpart with respect to P3-graphs for Whitney's result on line graphs.@ 1996 John Wiley & Sons, Inc.
π SIMILAR VOLUMES
A Cayley graph Cay(G, S) of a group G is called a CI-graph if whenever T is another subset of G for which Cay(G, S) βΌ = Cay(G, T ), there exists an automorphism Ο of G such that S Ο = T . For a positive integer m, the group G is said to have the m-CI property if all Cayley graphs of G of valency m a
A graph is a P 4 -indifference graph if it admits a linear ordering βΊ on its vertices such that every chordless path with vertices a, b, c, d and edges ab, bc, cd has either a βΊ b βΊ c βΊ d or d βΊ c βΊ b βΊ a. P 4 -indifference graphs generalize indifference graphs and are perfectly orderable. We give a
A Cayley graph or digraph Cay(G, S) of a finite group G is called a CI-graph of G if, for any T/G, Cay(G, S)$Cay(G, T) if and only if S \_ =T for some \_ # Aut(G). We study the problem of determining which Cayley graphs and digraphs for a given group are CI-graphs. A finite group G is called a conne
## Abstract Let __q__ be a prime power, π½~__q__~ be the field of __q__ elements, and __k__,β__m__ be positive integers. A bipartite graph __G__β=β__G~q~__(__k__,β__m__) is defined as follows. The vertex set of __G__ is a union of two copies __P__ and __L__ of twoβdimensional vector spaces over π½~__
The issue of when two Cayley digraphs on different abelian groups of prime power order can be isomorphic is examined. This had previously been determined by Anne Joseph for squares of primes; her results are extended.