Super edge-antimagic labelings of the path-like trees

Abstract

A graph G = (V, E) is (a, d)-edge-antimagic total if there exists a bijective function f : V(G) ∪ E(G) → {1, 2,..., |V(G)| + |E(G)|) such that the edge-weights w(uv) = f(u) + f(v) + f(uv),uv ∈ E(G), form an arithmetic progression with initial term a and common difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In this paper we study super (a, d)-edge-antimagic properties of paths and path-like trees.