NDC Pebbling Number for Some Class of Graphs

Title

NDC Pebbling Number for Some Class of Graphs

Creator

Lourdusamy A.; Dhivviyanandam I.; Mathew L.

Description

Let G be a connected graph. A pebbling move is defined as taking two pebbles from one vertex and the placing one pebble to an adjacent vertex and throwing away the another pebble. A dominating set D of a graph G = (V, E) is a non-split dominating set if the induced graph < V ? D > is connected. The Non-split Domination Cover(NDC) pebbling number, ?ns(G), of a graph G is the minimum of pebbles that must be placed on V(G) such that after a sequence of pebbling moves, the set of vertices with a pebble forms a non-split dominating set of G, regardless of the initial configuration of pebbles. We discuss some basic results and determine ?ns for some families of standard graphs. 2024 the Author(s), licensee Combinatorial Press.

Source

Journal of Combinatorial Mathematics and Combinatorial Computing, Vol-119, pp. 121-128.

Date

2024-01-01

Publisher

Charles Babbage Research Centre

Subject

Cover pebbling number; NDC pebbling number; Non-split dominating set

Coverage

Lourdusamy A., Department of Mathematics, St. Xaviers College (Autonomous), Palayamkottai, India; Dhivviyanandam I., St. Xaviers College (Autonomous), Palayamkottai Affiliated to Manonmaniam Sundaranar University, Tamil Nadu, Abisekapatti, 627012, India; Mathew L., Department of Mathematics CHRIST(Deemed to be university), Pune- Lavasa Campus, India

Rights

All Open Access; Hybrid Gold Open Access

Relation

ISSN: 8353026

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.61091/jcmcc119-13

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