Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9513246 | Discrete Mathematics | 2005 | 15 Pages |
Abstract
For a bridgeless connected graph G, let D(G) be the family of its strong orientations; and for any DâD(G), we denote by d(D) its diameter. The orientation number dâ(G) of G is defined by dâ(G)=min{d(D)|DâD(G)}. For a connected graph G of order n and for any sequence of n positive integers (si), let G(s1,s2,â¦,sn) denote the graph with vertex set V* and edge set E* such that V*=âi=1nVi, where Vi's are pairwise disjoint sets with |Vi|=si, i=1,2,â¦,n, and for any two distinct vertices x, y in V*, xyâE* if and only if xâVi and yâVj for some i,jâ{1,2,â¦,n} with iâ j such that vivjâE(G). We call the graph G(s1,s2,â¦,sn) a G vertex multiplication. In this paper, we determine the orientation numbers of various cycle vertex multiplications.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
K.L. Ng, K.M. Koh,