Odd harmonious labeling of step ladder graphs

Abstract

A graph G(p,q) is said to be odd harmonious if there exists an injection f: V(G) → { 0, 1, 2, • • •, 2q — 1} such that the induced function f*: E(G) → { 1, 3, • • •, 2q -1} defined by f*(uv) = f(u) + f(v) is a bijection. In this paper we prove that path union of t copies of S(T_n) , double sided step ladder 2S (T_2×n), path union of t copies of 2S (T_2×n), S(t.C_bn), S (tC₄), C₄^t, C₆^t* and C₈^t are odd harmonious graphs. © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.