The Pendant Number ofLine Graphs andTotal Graphs

Title

The Pendant Number ofLine Graphs andTotal Graphs

Creator

Kottarathil J.; Naduvath S.; Kureethara J.V.

Description

The parameter, pendant number of a graph G, is defined as the least number of end vertices of paths in a path decomposition of the given graph and is denoted as ? p(G). This paper determines the pendant number of regular graphs, complete r-partite graphs, line graphs, total graphs and line graphs of total graphs. We explore the bougainvillea graphs, e-pendant graphs and v-pendant graphs. If the pendant number is 2, then the number of paths in the path decomposition of the given graph is at most ? (G), the maximum degree of the graph. Hence, a large class of graphs give a more reasonable solution to Gallais conjecture on number of paths in the given path decomposition. 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

Source

Lecture Notes in Networks and Systems, Vol-462, pp. 457-468.

Date

2022-01-01

Publisher

Springer Science and Business Media Deutschland GmbH

Subject

e-pendant graph; Gallai conjecture; Path decomposition; v-pendant graph

Coverage

Kottarathil J., St. Josephs College, Kerala, Moolamattom, 685591, India; Naduvath S., Christ University, Bangalore, India; Kureethara J.V., Christ University, Bangalore, India

Rights

Restricted Access

Relation

ISSN: 23673370; ISBN: 978-981192210-7

Format

Online

Language

English

Type

Conference paper

Identifier

https://doi.org/10.1007/978-981-19-2211-4_41

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