On Leech labelings of graphs and some related concepts

Title

On Leech labelings of graphs and some related concepts

Creator

Lakshmanan S. A.; Eldho M.M.

Description

Let G=(V,E) be a graph and let f:E?{1,2,3,} be an edge labeling of G. The path weight of a path P in G is the sum of the labels of the edges of P and is denoted by w(P). The path number of G, tp(G) is the total number of paths in a graph G. If the set of all path weights S in G with respect to the labeling f is {1,2,3,,tp(G)}, then f is called a Leech labeling of G. A graph which admits a Leech labeling is called a Leech graph. Leech index is a parameter which evaluates how close a graph is towards being Leech. In this paper, the path number of the wheel graph Wn is obtained. We also determine a bound for the Leech index of Wn and a subclass of unicyclic graphs. A python program that gives all possible Leech labelings of a cycle Cn for n?3, if it exists, is also provided. 2023 Elsevier B.V.

Source

Discrete Mathematics, Vol-347, No. 4

Date

2024-01-01

Publisher

Elsevier B.V.

Subject

Leech graph; Leech index; Leech labeling; Path number

Coverage

Lakshmanan S. A., Department of Mathematics, Cochin University of Science and Technology, Kerala, Cochin, 22, India; Eldho M.M., Department of Mathematics, CHRIST (Deemed to be University), Kerala, Bangalore, India

Rights

Restricted Access

Relation

ISSN: 0012365X; CODEN: DSMHA

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1016/j.disc.2023.113837

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