## Abstract Let __G__ be a 4βregular 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 GrΓΆtzschβSachs graphs
On chromatic uniqueness of two infinite families of graphs
β Scribed by Feng-Ming Dong
- Publisher
- John Wiley and Sons
- Year
- 1993
- Tongue
- English
- Weight
- 229 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
In this paper, it is proven that for each k β₯ 2, m β₯ 2, the graph Ξ~k~(m,β¦,m), which consists of k disjoint paths of length m with same ends is chromatically unique, and that for each m, n, 2 β€ m β€ n, the complete bipartite graph K~m,n~ is chromatically unique. Β© 1993 John Wiley & Sons, Inc.
π SIMILAR VOLUMES
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.
## Abstract The fractional chromatic number of a graph __G__ is the infimum of the total weight that can be assigned to the independent sets of __G__ in such a way that, for each vertex __v__ of __G__, the sum of the weights of the independent sets containing __v__ is at least 1. In this note we g
Frucht and Giudici classified all graphs having quadratic a-polynomials. Here w e classify all chromatically unique graphs having quadratic (Tpolynomials.
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