Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2010-07-01

Journal: ARS COMBINATORIA

Included Journals: Scopus、SCIE

Volume: 96

Page Number: 33-40

ISSN: 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.