On the strength of some trees

AKCE International Journal of Graphs and Combinatorics

Rikio Ichishima¹  Francesc A. Muntaner-Batle²  Akito Oshima² 

[1] Department of Sport and Physical Education, Faculty of Physical Education, Kokushikan University;Graph Theory and Applications Research Group, School of Electrical Engineering and Computer Science, Faculty of Engineering and Built Environment, The University of Newcastle;

关键词: strength;    caterpillar;    tree;    graph labeling;    corona;   

DOI  :  10.1016/j.akcej.2019.06.002

来源: DOAJ

【 摘 要 】

Let be a graph of order . A numbering of is a labeling that assigns distinct elements of the set to the vertices of , where each edge of is labeled . The strength str of a numbering of is defined by that is, is the maximum edge label of , and the strength str of a graph itself is The strengths and are determined for caterpillars and -level complete -ary trees . The strength is also given for graphs obtained by taking the corona of certain graphs and an arbitrary number of isolated vertices. The work of this paper suggests an open problem on the strength of trees.

【 授权许可】

Unknown