## Abstract We investigate the conjecture that every circulant graph __X__ admits a __k__‐isofactorization for every __k__ dividing |__E__(__X__)|. We obtain partial results with an emphasis on small values of __k__. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 406–414, 2006
On the cycle-isomorphism of graphs
✍ Scribed by Xingxing Yu
- Publisher
- John Wiley and Sons
- Year
- 1991
- Tongue
- English
- Weight
- 336 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
This paper considers conditions ensuring that cycle‐isomorphic graphs are isomorphic. Graphs of connectivity ⩾ 2 that have no loops were studied in [2] and [4]. Here we characterize all graphs G of connectivity 1 such that every graph that is cycle‐isomorphic to G is also isomorphic to G.
📜 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) ∼ = Cay(G, T ), there exists an automorphism σ of G such that S σ = 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
## Abstract Let __G__ and __H__ be 2‐connected 2‐isomorphic graphs with __n__ nodes. Whitney's 2‐isomorphism theorem states that __G__ may be transformed to a graph __G__\* isomorphic to __H__ by repeated application of a simple operation, which we will term “switching”. We present a proof of Whitn
Let G be a finite group, S a subset of G=f1g; and let Cay ðG; SÞ denote the Cayley digraph of G with respect to S: If, for any subset T of G=f1g; CayðG; SÞ ffi CayðG; T Þ implies that S a ¼ T for some a 2 AutðGÞ; then S is called a CI-subset. The group G is called a CIM-group if for any minimal gene
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
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.