Some New Classes of k-distance Trees with Alpha Labeling

Dedas Mishra¹ , Sushant Kumar Rout² , Subarna Bhattacharjee³

Section:Research Paper, Product Type: Journal-Paper
Vol.7 , Issue.4 , pp.26-34, Aug-2020

Online published on Aug 31, 2020

Copyright © Dedas Mishra, Sushant Kumar Rout, 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 :
By a k- distance tree we mean a tree T which possesses a path H with the condition that each vertex of T is at a distance at most k from H. By a graceful labelling of a tree T we mean a bijection f of the vertices of T, i.e V(T) into the set {0,1,2,...,|V(T)|} with the condition that the set of the labels of the edges constitutes the set {1,2,3,...,|V(T)|- 1}, where the label of each edge (a,b) in T is defined by |f(a) ? f(b)|. An a - labelling of a tree T is a graceful labelling f of T if there exists an integer r > 0 for which we have either f(a) < r ≤ f(b) or f(b) < r ≤ f(a) for each edge (a,b) of T. In this paper we use techniques to associate two or more graceful trees and construct a generalized class of trees, namely k ? distance trees that possess a - labelling

Key-Words / Index Term :
graceful labeling, a - labeling, k-distance trees

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