Total coalitions of cubic graphs of order at most 10 Full article
| Journal |
Communications in Combinatorics and Optimization
ISSN: 2538-2128 , E-ISSN: 2538-2136 |
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| Output data | Year: 2025, Volume: 10, Number: 3, Pages: 601-615 Pages count : 15 DOI: 10.22049/CCO.2024.29015.1813 | ||||
| Tags | coalition, total coalition, cubic graphs, Petersen graph. | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 |
Министерство науки и высшего образования РФ Mathematical Center in Akademgorodok |
075-15-2019-1613, 075-15-2022-281 |
Abstract:
A total coalition in a graph G = (VE) consists of two disjoint sets of vertices V1 and V2, neither of which is a total dominating set but whose union V1 V2, is a total dominating set. A total coalition partition in a graph G of order n = V is a vertex partition = V1 V2 Vk such that every set Vi dominating set but forms a total coalition with another set Vj is not a total which is not a total dominating set. The total coalition number TC(G) equals the maximum order k of a total coalition partition of G. In this paper, we determine the total coalition number of all cubic graphs of order n 10.
Cite:
Golmohammadi H.
Total coalitions of cubic graphs of order at most 10
Communications in Combinatorics and Optimization. 2025. Т.10. №3. С.601-615. DOI: 10.22049/CCO.2024.29015.1813 WOS Scopus
Total coalitions of cubic graphs of order at most 10
Communications in Combinatorics and Optimization. 2025. Т.10. №3. С.601-615. DOI: 10.22049/CCO.2024.29015.1813 WOS Scopus
Dates:
| Submitted: | Sep 27, 2023 |
| Accepted: | Jan 25, 2024 |
| Published online: | Jan 30, 2024 |
| Published print: | Jan 20, 2025 |
Identifiers:
| Web of science: | WOS:001155718900001 |
| Scopus: | 2-s2.0-105007057629 |