A total labellings of m triangles

Abstract

Assume that we have $m$ triangles. In this paper, we discuss certain labelling of the $m$ triangles called $c$-Erd\"osian for some positive integers $c$. We regard labellings of the vertices of the triangles by positive integers, which induce the edge labels for the triangles as the sum of the two incident vertex labels. They have the property that each vertex label and edge label appears only once in the set of positive integers $\{c,\ldots ,c+6m-1\}$. Here, we show how to construct certain $c$-Erd\"osian of $m$ triangles.