The 2-Tuple Domination Problem on Circular-arc Graphs

Sinha, Angshu Kumar; Rana, Akul; Pal, Anita

doi:10.22457/jmi.v8a6

Cited by 3 publications

(3 citation statements)

References 7 publications

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“…Mitchell and Hedetniemi [7] and Xu [14] have worked on edge domination parameter. In 2014, Sinha et al [9] have studied about 2-tuple domination problem on trapezoid graphs. In [8,10] have studied about total domination related parameters and in [1,13] have found some results on signed edge domination parameters.…”

Section: G Gmentioning

confidence: 99%

Signed Edge Total Domination on Rooted Product Graphs

Rani¹,

Begum²,

Raju³

2018

APAM

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Let G be a rooted product graph of path with a cycle graph with the vertex set V and the edge set E. Here n P be a Path with n vertices and m C (3) m ≥ be a cycle with a sequence of n rooted graphs m1 m2 m3 mn C ,C ,C ,-,C. We call n m P (C) the rooted product of n P by m C and it is denoted by n m P C o. Every i th vertex of n P is merging with any one vertex in every i th copy of m C. In this paper we discuss some results on rooted product graph of path with a cycle graph.

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Section: G Gmentioning

confidence: 99%

Signed Edge Total Domination on Rooted Product Graphs

Rani¹,

Begum²,

Raju³

2018

APAM

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“…The concept of edge domination was introduced by Mitchell and Hedetniemi [13]. Domination and its variations have been extensively studied in the literature, see [1,6,11,12,17,21,22,25,26] …”

Section: Introductionmentioning

confidence: 99%

Edge Roman Star Domination Number on Graphs

Sinha¹,

Rana²,

Pal³

2017

APAM

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“…For general circular-arc graphs -which generalize proper interval graphsefficient algorithms are presented for 1-tuple domination in [5] and for the 2-tuple domination in a recent work [14]. Efficient algorithms are known to solve the 1-tuple domination problem [5,9] and the 1-tuple total domination problem [4], but their complexity are not known for any k greater than 1.…”

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confidence: 99%

k-tuple and k-tuple total dominations on web graphs

Dobson¹,

Leoni²,

Pujato³

2022

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In this work we address k-tuple and k-tuple total dominations on the subclass of circular-arc graphs given by web graphs. For the non total version, we present a linear time algorithm based on the regularity of the closed neighborhoods associated with web graphs which allows the use of modular arithmetic for integer numbers. For the total version, we derive bounds for this graph class. PreliminariesDomination in graphs is useful in different applications. There exist many variations -such as k-tuple domination and k-tuple total domination, among others-regarding slight differences in their definitions. These differences make circular-arc graph subclasses adequate and useful mostly due to their relation to "circular" issues, such as in forming sets of representatives, in resource allocation in distributed computing systems,

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The 2-Tuple Domination Problem on Circular-arc Graphs

Abstract: Given a simple graph .

Cited by 3 publications

References 7 publications

Signed Edge Total Domination on Rooted Product Graphs

Signed Edge Total Domination on Rooted Product Graphs

Edge Roman Star Domination Number on Graphs

k-tuple and k-tuple total dominations on web graphs

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