On the strength of some trees

Abstract

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.

Keywords

• strength
• caterpillar
• tree
• graph labeling
• corona