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Indexed by:期刊论文

Date of Publication:2009-06-01

Journal:INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS

Included Journals:SCIE、Scopus

Volume:40

Issue:3

Page Number:155-181

ISSN No.:0019-5588

Key Words:Irregular total labelling; generalized Petersen graph; ladder; Knodel graph; flower snark

Abstract:An edge (A vertex) irregular total k-labelling of a graph G is such a labelling of the vertices and edges with integers 1, ..., k that the weights of any two different edges (vertices) are distinct, where the weight of an edge (a vertex) is the sum of the label of the edge (vertex) itself and the labels of its incident vertices (edges). The minimum k for which the graph G has an edge (a vertex) irregular total k-labelling is called the total edge (vertex) irregularity strength of the graph G, tes (G) (tvs (G)). In this paper, we show the exact values of tes (G) and tvs (G) of some families of graphs, including the generalized Petersen graph P (n, k), ladder L(n), Mobius ladder M(n), Knodel graph W(3,n), and flowur snark and related graph.