On Some Graphs Whose Domination Number Is thePerfect Italian Domination Number

Title

On Some Graphs Whose Domination Number Is thePerfect Italian Domination Number

Creator

Poovathingal A.; Kureethara J.V.

Description

Perfect Italian Domination (PID) is a vertex labelling of a graph G by numbers from the set such that a vertex in G labelled 0 has a neighbourhood where the summation of the labels of the vertices in it is precisely 2. The summation of labels on the vertices of the graph which satisfy the PID labelling is known as its PID number, and is the minimum possible PID number of a graph G. We find some characterization of graphs for which . We also find a lower bound for |V(G)|, which satisfies the same. Further, we discuss the graphs that satisfies or . A realisation problem is used to prove that PID cannot be bounded by a scalar multiple of the Domination number. The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.

Source

Lecture Notes in Networks and Systems, Vol-869 LNNS, pp. 191-200.

Date

2024-01-01

Publisher

Springer Science and Business Media Deutschland GmbH

Subject

Domination number; Independent set; Join operator; perfect italian domination

Coverage

Poovathingal A., Department of Mathematics, Christ University, Bangalore, India; Kureethara J.V., Department of Mathematics, Christ University, Bangalore, India

Rights

Restricted Access

Relation

ISSN: 23673370; ISBN: 978-981999039-9

Format

Online

Language

English

Type

Conference paper

Identifier

https://doi.org/10.1007/978-981-99-9040-5_13

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