| Title: | On independent coalition in graphs and independent coalition graphs |
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| Authors: | ID Alikhani, Saeid (Author)
ID Bakhshesh, Davood (Author)
ID Golmohammadi, Hamidreza (Author)
ID Klavžar, Sandi (Author) |
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| Files: |  PDF - Presentation file, download (157,79 KB)
MD5: 8E4F9FEA681D3CB726E06E9DA36538B1
 URL - Source URL, visit https://www.dmgt.uz.zgora.pl/publish/article.php?doi=2543
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | An independent coalition in a graph $G$ consists of two disjoint, independent vertex sets $V_1$ and $V_2$, such that neither $V_1$ nor $V_2$ is a dominating set, but the union $V_1\cup V_2$ is an independent dominating set of $G$. An independent coalition partition of $G$ is a partition $\{V_1, \ldots, V_k\}$ of $V(G)$ such that for every $i\in [k]$, either the set $V_i$ consists of a single dominating vertex of $G$, or $V_i$ forms an independent coalition with some other part $V_j$. The independent coalition number $IC(G)$ of $G$ is the maximum order of an independent coalition of $G$. The independent coalition graph ${\rm ICG}(G,\pi)$ of $\pi=\{V_1, \ldots, V_k\}$ (and of $G$) has the vertex set $\{V_1,\ldots, V_k\}$, vertices $V_i$ and $V_j$ being adjacent if $V_i$ and $V_j$ form an independent coalition in $G$. In this paper, a large family of graphs with $IC(G) = 0$ is described and graphs $G$ with $IC(G)\in \{n(G), n(G)-1\}$ characterized. Some properties of ${\rm ICG}(G,\pi)$ are presented. The independent coalition graphs of paths are characterized, and the independent coalition graphs of cycles described. |
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| Keywords: | dominating set, independent set, independent coalition, independent coalition number, independent coalition graphs |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | str. 533-544 |
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| Numbering: | Vol. 45, no. 2 |
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| PID: | 20.500.12556/DiRROS-21951  |
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| UDC: | 519.17 |
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| ISSN on article: | 1234-3099 |
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| DOI: | 10.7151/dmgt.2543 |
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| COBISS.SI-ID: | 232324611 |
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| Note: |
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| Publication date in DiRROS: | 11.04.2025 |
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| Views: | 617 |
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| Downloads: | 356 |
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