Leech labeling problem on tristar

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 call...

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Bibliographic Details
Main Authors: Varghese, Seena, Savithri, Aparna Lakshmanan, Arumugam, Subramanian
Format: Conference Proceeding
Language:English
Subjects:
Labelling
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Summary: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 prove that a tristar of diameter 4 is not a Leech tree. The Leech index of bistars and tristars is also given.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0114834