A result on the strength of graphs by factorizations of complete graphs | [Discrete Mathematics Letters • 2022]

Author(s):

1. Rikio Ichishima: Department of Sport and Physical Education, Faculty of Physical Education, Kokushikan Universityty, 7-3-1 Nagayama, Tama-shi, Tokyo,Japan

2. Francesc A. Muntaner-Batle: Graph Theory and Applications Research Group, School of Electrical Engineering and Computer Science, Faculty of Engineering and Built Environment,The University of Newcastle, NSW 2308, Australia

3. Akito Oshima: Graph Theory and Applications Research Group, School of Electrical Engineering and Computer Science, Faculty of Engineering and Built Environment,The University of Newcastle, NSW 2308, Australia

Abstract:

A numbering f of a graph G of order n is a labeling that assigns distinct elements of the set f1; 2; : : : ; ng to the vertices of G. The strength of G is defined by str (G) = min fstrf (G) j f is a numbering of Gg ,where strf (G) = max ff (u) + f (v) j uv 2 E (G)g. In this paper, some results obtained from factorizations of complete graphs are presented. In particular, it is shown that for every k 2 [1; n ?? 1], there exists a graph G of order n satisfying (G) = k and str (G) = n + k, where (G) denotes the minimum degree of G.

Page(s): 78-82

DOI: 10.47443/dml.2021.0096

Published: Journal: Discrete Mathematics Letters, Volume: 8, Issue: 0, Year: 2022

Keywords:

strength , graph labeling , combinatorial optimization , factorization

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