Vol. 9(2) July 2021, No. 24, pp. 288-294.

(1,N )-ARITHMETIC LABELLING OF CHAIN OF EVEN CYCLES, SPLITTING GRAPH OF PATHS AND SPLITTING GRAPH OF CYCLES C4m
Vol. 9(2) July 2021, No. 24, pp. 288-294
S. ANUBALA AND V.RAMACHANDRAN

 

Abstract

A (p,q) - graph G is said to have (1, N) - Arithmetic labelling if there is a one-one function φ from the vertex set V (G) to {0, 1, N, (N + 1) , 2N, (2N + 1) , ..., (q − 1) N, (q − 1) (N + 1)} 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.


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