(1,N)-ARITHMETIC LABELLING OF CHAIN OF EVEN CYCLES, SPLITTING GRAPH OF PATHS AND SPLITTING GRAPH OF CYCLES C4m.

A (p,q) - graph G is said to have (1;N) - Arithmetic labelling if there is a one-one function from the vertex set V (G) to f0; 1;N; (N + 1); 2N; (2N + 1); :::; (q 1)N; (q 1) (N + 1)g so that the values of the edges, obtained as the sums of the labelling assigned to their end vertices can be arranged in the arithmetic progression 1; (N + 1); (2N + 1); :::; (q 1)N +1: In this paper we prove that certain chain of even cycles, splitting graph of paths and splitting graph of cycles C4m have (1,N) - Arithmetic Labelling for every positive integer N > 1. [ABSTRACT FROM AUTHOR]