منابع مشابه
Isomorphisms of P4-graphs
For graphs G and G' with minimum degree is = 3 and satisfying one of two other conditions, we prove that any isomorphism from the P4 -graph P4 (G) to P4 ( G') can be induced by a vertex-isomorphism of G onto G'. We also prove that a connected graph G is isomorphic to its P4 -graph P4 (G) if and only if G is a cycle of length at least 4.
متن کاملOn Isomorphisms of Vertex-transitive Graphs
The isomorphism problem of Cayley graphs has been well studied in the literature, such as characterizations of CI (DCI)-graphs and CI (DCI)-groups. In this paper, we generalize these to vertex-transitive graphs and establish parallel results. Some interesting vertex-transitive graphs are given, including a first example of connected symmetric non-Cayley non-GI-graph. Also, we initiate the study...
متن کاملIsomorphisms of Cayley graphs on nilpotent groups
Let S be a finite generating set of a torsion-free, nilpotent group G. We show that every automorphism of the Cayley graph Cay(G;S) is affine. (That is, every automorphism of the graph is obtained by composing a group automorphism with multiplication by an element of the group.) More generally, we show that if Cay(G1;S1) and Cay(G2;S2) are connected Cayley graphs of finite valency on two nilpot...
متن کاملOn Isomorphisms of Finite Cayley Graphs
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 Sσ = 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 are CI-graphs; further, if G has the k-CI property for all k ≤ m, then G is called an m-CI-group, an...
متن کاملP3-isomorphisms for graphs
The P3-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 P3-graphs are either isomorphic or part of three exceptional families. We also characterize all isomorphisms between P3-graphs...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1984
ISSN: 0012-365X
DOI: 10.1016/0012-365x(84)90153-5