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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Aparna Lakshmanan S
Department of Mathematics, St.Xavier's College for Women, Aluva -683101, Kerala, India
Electrical & Electronics Engineering

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Two classes of non-Leech trees Seena Varghese; Aparna Lakshmanan S; Subramanian Arumugam
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 8, No 1 (2020): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2020.8.1.15

Abstract

Let T be a tree of order n. For any edge labeling f : E → {1,2,3,...} the weight of a path P is the sum of the labels of the edges of P and is denoted by w(P). If the weights of the nC2 paths in T are exactly 1, 2,...,nC2, then f is called a Leech labeling and a tree which admits a Leech labeling is called a Leech tree. In this paper we determine all Leech trees having diameter three. We also prove that the tree obtained from the path Pn =(v1,v2,...,vn) by attaching a pendent vertex at vn-1 is not a Leech tree for all n ≥ 4.
Co-Authors Seena Varghese Subramanian Arumugam