Реферат: Let G be a graph of minimum degree at least two. A set D of vertices of a graph G with the vertex set V is a double total dominating set of G, if every vertex v has at least two neighbors in D. A double total coalition consists of two disjoint sets of vertices V1 and V2, neither of which is a double total dominating set but their union V1∪V2 is a double total dominating set. A double total coalition partition of a graph Gis a partition Θ = {V1,V2,...,Vk} of V such that no subset of Θ is a double total dominating set of G, but for every set Vi ∈ Θ, there exists a set Vj ∈ Θ such that Vi and Vj form a double total coalition. In this paper we initiate the study of the double total coalition by setting some basic results, giving exact values and bounds for the double total coalition number.

Библиографическая ссылка: Golmohammadi H. , Alikhani S. , Bakhshesh D.
Double total coalitions in graphs
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2025. V.22. N2. P.1497–1506. DOI: 10.33048/semi.2025.22.090 Scopus

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Поступила в редакцию:	23 апр. 2025 г.
Опубликована в печати:	9 дек. 2025 г.
Опубликована online:	9 дек. 2025 г.

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Scopus:

2-s2.0-105024787653

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