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L(3,1)LABELING AND L’ (3,1) LABELING OF MERGE GRAPH(C3* K1,n), SUBDIVISION OF THE EDGES OF THE STAR GRAPH, (K1,n), AND L(3,1) LABELING OF TADPOLE GRAPH T(3,n) AND LILLY GRAPH In

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A.S.Shanthi, Fathima Azher
» doi: 10.31838/ecb/2023.12.s3.677

Abstract

????(3,1) labeling is one of a particular model of frequency assignment problem of ????(ℎ, ????) labeling. A ????(3,1) labeling of a graph ???? is a function ???? from the vertex set ????(????) to the set of positive integers such that for any two vertices ????, ???? if ????(????, ????)=1 then |????(????) − ????(????)| ≥ 3 and if ????(????, ????)=2 then |????(????) − ????(????)| ≥ 1. In ????(3,1) labeling, ???? is the smallest positive integer which denotes the maximum label used. ????′(3,1) labeling is an injective ????(3,1) labeling and ????′ denotes the smallest positive integer which denotes the maximum label used in ????′(3,1) labeling. In this paper, we consider ????(3,1) labeling and ????′(3,1) labeling of Merge graph(????3 ∗ ????1,????), Subdivision of the edges of the star graph ????1,????, and ????(3,1) labeling of Tadpole graph ????(3, ????) and Lilly graph ????????.

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