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Indexed by:期刊论文

Date of Publication:2010-07-01

Journal:ARS COMBINATORIA

Included Journals:SCIE、Scopus

Volume:96

Page Number:33-40

ISSN No.:0381-7032

Key Words:(d, 1)-Total labelling; Minimum span; Flower snark

Abstract:A (d, 1)-total labelling of a graph G is an assignment of integers to V(G) boolean OR E(G) such that: (i) any two adjacent vertices of G receive distinct integers, (ii) any two adjacent edges of G receive distinct integers, and (iii) a vertex and its incident edge receive integers that differ by at least d in absolute value. The span of a (d, 1)-total labelling is the maximum difference between two labels. The minimum span of labels required for such a (d, 1)-total labelling of C is called the (d,1)-total number and is denoted by lambda(T)(d) (G). In this paper, we prove that lambda(T)(d)(G) >= d+r+1 for r-regular nonbipartite graphs with d >= r >= 3 and determine the (d,1)-total numbers of flower snarks and of quasi flower snarks.