On the secure vertex cover pebbling number

Title

On the secure vertex cover pebbling number

Creator

Hurlbert G.H.; Mathew L.; Quadras J.; Surya S.S.

Description

A new graph invariant called the secure vertex cover pebbling number, which is a combination of two graph invariants, namely, secure vertex cover and cover pebbling number, is introduced in this paper. The secure vertex cover pebbling number of a graph, G, is the minimum number m so that every distribution of m pebbles can reach some secure vertex cover of G by a sequence of pebbling moves. In this paper, the complexity of the secure vertex cover problem and secure vertex cover pebbling problem are discussed. Also, we obtain some basic results and the secure vertex cover pebbling number for complete r-partite graphs, paths, Friendship graphs, and wheel graphs. 2023 World Scientific Publishing Co. Pte Ltd. All rights reserved.

Source

Asian-European Journal of Mathematics, Vol-16, No. 10

Date

2023-01-01

Publisher

World Scientific

Subject

cover pebbling number; Graph pebbling; secure vertex cover

Coverage

Hurlbert G.H., Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, VA, United States; Mathew L., CHRIST (Deemed to be University), Lavasa Campus Lavasa, Maharashtra, Pune, India; Quadras J., Department of Mathematics Maris Stella College (Autonomous), Vijayawada, India; Surya S.S., Department of Mathematics, Stella Maris College (Autonomous), India Affiliated to the University of Madras, Chennai, India

Rights

All Open Access; Green Open Access

Relation

ISSN: 17935571

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1142/S1793557123501826

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