ON SUPER (A, D)-EDGE-ANTIMAGIC TOTAL LABELING OF GENERALIZED EXTENDED W-TREES

Let G = (V(G), E(G)) be a graph with v vertices and e edges. An (a, d)-edge antimagic total labeling is a bijection gimel: V(G) boolean OR E(G) -> {1, 2,...,v broken vertical bar e}, such that the set of edge weights {w(xy): w(xy) = gimel(x)+ gimel(y) + gimel(xy), xy is an element of E(G)} forms an arithmetic progression with the initial term a and common difference d. Additionally, if gimel(V(G))={1,2,...,v} then gimel is a super (a,d)-edge-antimagic total labeling. In this paper, we define a generalized extended w-tree denoted by GEwt ( n(1,) n(2), ..., n(k), m(1), m(2), ..., m(k); r;k) and prove that it admits a super (a,b) - EAT labeling.