(k, d) Graceful Labelling of Some New Families of Graphs Derived from Cyclic Firecrackers

Dedas Mishra¹ , Gobind Mohanty² , Subarna Bhattacharjee³

Section:Research Paper, Product Type: Journal-Paper
Vol.9 , Issue.3 , pp.35-42, Jun-2022

Online published on Jun 30, 2022

Copyright © Dedas Mishra, Gobind Mohanty, Subarna Bhattacharjee . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
A graph H containing t edges is said to possess a (k,d) graceful labelling if there exist positive integers k and d and an injection f? V (H)?{0,1,..,k +(t-1)d} so that the mapping g? E(G) ?{k+sd,s =0,1,2,…t-1} defined by g(x,y) = |f(x) - f(y)|, for any (x,y) ?E(G), is surjective. A cyclic firecracker is a graph which is denoted as C_n? K_(m_i,1,1),i = 1,2,...,n, m_i ?0 is a graph consisting of one cycle C_n and each vertex of C_n is attached to the center of some star. Here we identify a family of (k,d) graceful graphs derived from cyclic firecrackers.

Key-Words / Index Term :
(k, d)-graceful Labeling, firecracker, cyclic firecrackers.

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