Abstract
Let G be a graph of order p. A numbering f of G is a labeling that assigns distinct elements of the set 1,2,…,p to the vertices of G, where each edge uv of G is labeled fu+fv. The strength strfG of a numbering f:VG→1,2,…,p of G is defined by strfG=maxfu+fvuv∈EG,that is, strfG is the maximum edge label of G, and the strength strG of a graph G itself is strG=minstrfGf is a numbering of G.The strengths strT and strTn,k are determined for caterpillars T and k-level complete n-ary trees Tn,k. The strength strG is also given for graphs G 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.
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