The strength of graphs and related invariants
Rikio Ichishima, Francesc Antoni Muntaner-Batle, Akito Oshima, Yukio Takahashi · Institutional Repositories DataBase (IRDB) · 2020
A numbering f of a graph G of order n is a labeling that assigns distinct elements of the set { 1, 2, . . . , n} to the vertices of G. The strength of G isstr (G) = min { str_f (G) |f is a numbering of G},where str_f (G) = max {f (u) + f (v) |uv ∈E (G) }. In this paper, we introduce the concept of anti-strength astr (G), and establish that str (G) + astr (G) = 2 (n + 1) for a nonempty graph G of order n. In addition, we show how the strength (or anti-strength) of a graph and other invariants defined on graphs are related.