Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 8, No 1 (2020): Electronic Journal of Graph Theory and Applications

Two classes of non-Leech trees

Seena Varghese (Department of Mathematics, Federal Institute of Science and Technology, Angamaly - 683577, Kerala, India.)
Aparna Lakshmanan S (Department of Mathematics, St.Xavier'
s College for Women, Aluva -683101, Kerala, India)
Subramanian Arumugam (National Centre for Advanced Research in Discrete Mathematics, Kalasalingam Academy of Research and Education, Anand Nagar, Krishnankoil-626126, Tamilnadu, India)

Article Info

Publish Date
01 Apr 2020

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.

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Journal Info
Electronic Journal of Graph Theory and Applications (EJGTA)
Website

Abbrev

ejgta

Publisher

Indonesian Combinatorial Society

Subject

Electrical & Electronics Engineering

Description

The Electronic Journal of Graph Theory and Applications (EJGTA) is a refereed journal devoted to all areas of modern graph theory together with applications to other fields of mathematics, computer science and other sciences. The journal is published by the Indonesian Combinatorial Society ...