It is proved that given any number of graphs of order at most n, the sphericity of their join does not exceed 2(n-1). We introduce an adjacency relation into Euclidean n-space E" so that it may be regarded as an infinite graph: Two points x and y of E" are defined to be adjacent if and only if 0<[x
On the sphericity of the graphs of semiregular polyhedra
β Scribed by Hiroshi Maehara
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 272 KB
- Volume
- 58
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
The sphericity of a graph G is the smallest integer n such that G can be represented as the intersection graph of a family of unit-diameter spheres in Euclidean n-space E n. We determine here the sphericities of the graph of semiregular polyhedra in E 3 except a few prisms.
π SIMILAR VOLUMES
## Abstract An ({__r__, __r__ + 1}; __g__)βcage is a graph with degree set {__r__, __r__ + 1}, girth __g__, and with the smallest possible order; every such graph is called a semiregular cage. In this article, semiregular cages are shown to be maximally edgeβconnected and 2βconnected. As a conseque
Given a simple connected graph G, let K(n) [2(n)] be the minimum cardinality of a set of vertices [edges], if any, whose deletion disconnects G and every remaining component has more than n vertices. For instance, the usual connectivity and the superconnectivity of G correspond to x(0) and ~c(1 ), r