Author:
Kriegel Klaus,Pöschel Reinhard,Wessel Walter
Abstract
Every finite loopless undirected graph G is isomorphic to an induced subgraph of a suitable finite direct power of the undirected graph G0 with two adjacent vertices 0,1 and one loop at vertex 1. The least natural number m such that G can be represented in this way is called its G0-dimension. We give some upper and lower bounds of this dimension depending on certain other graph invariants and determine its exact values for some special classes of graphs. Some methods to determine a concrete G0-representation, that is an embedding of G into , are presented. Moreover we show that the problem of determining the G0-dimension of a graph is NP-complete.
Publisher
Cambridge University Press (CUP)
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