Introduction to total coalitions in graphs

2022/11/21 by ‎Saeid Alikhani, Alikhani, Saeid, Bakhshesh, Davood +1 · 6 citations
Computer Science · #05C60 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2211.11590

openalex publication_date 2022/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a graph with vertex set V. Two disjoint sets V₁, V₂⊆ V are called a total coalition in G, if neither V₁ and V₂ is a total dominating set of G but V₁∪ V₂ is a total dominating set. A total coalition partition of G is a vertex partition π=\V₁,V₂,…, V_k\ such that no set of π is a total dominating set but each set V_i∈ π forms a total coalition with another set V_j∈ π. The maximum cardinality of a total coalition partition of G is called the total coalition number of G, denoted by TC(G). In this paper, we initiate the study of the total coalition in graphs and its properties.

Cited by

• Total outer-independent coalition in graphs
• Super Coalition Number in Graphs
• Secure coalitions in graphs
• On Coalition Graphs and Coalition Count of Graphs
• k-Fair Coalitions in Graphs
• Fair coalition in graphs

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• General sharp upper bounds on the total coalition number
• Total k-coalition: bounds, exact values and an application to double coalition
• k-Coalitions in Graphs
• On Coalition Graphs and Coalition Count of Graphs
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