Domination type parameters of Pell graphs

Özer, Arda Buğra; Saygı, Elif; Saygı, Zulfukar

doi:10.26493/1855-3974.2637.f61

Cited by 1 publication

(1 citation statement)

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“…The maximum number of classes of a domatic partition (idomatic partition) of G is called the domatic number (idomatic number) of G, denoted by d(G) (id(G)) The concepts of domination and domatic partition and their variations have been studied widely in the literature. See, for example, [1,2,3,4,5,6,12].…”

Section: Introductionmentioning

confidence: 99%

Independent coalition in graphs: existence and characterization

Samadzadeh,

Mojdeh

2024

Ars Math. Contemp.

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An independent coalition in a graph G consists of two disjoint sets of vertices V 1 and V 2 neither of which is an independent dominating set but whose union V 1 ∪ V 2 is an independent dominating set. An independent coalition partition, abbreviated, ic-partition, in a graph G is a vertex partition π = {V 1 , V 2 , . . . , V k } such that each set V i of π either is a singleton dominating set, or is not an independent dominating set but forms an independent coalition with another set V j ∈ π. The maximum number of classes of an ic-partition of G is the independent coalition number of G, denoted by IC(G). In this paper we study the concept of ic-partition. In particular, we discuss the possibility of the existence of ic-partitions in graphs and introduce a family of graphs for which no ic-partition exists. We also determine the independent coalition number of some classes of graphs and investigate graphs G of order n with IC(G) ∈ {1, 2, 3, 4, n} and the trees T of order n with IC(T ) = n − 1.

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