| Title: | Complete co-secure domination in graphs |
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| Authors: | ID Saraswathy, Gisha (Author)
ID Menon, Manju K. (Author) |
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| Files: |  ADAM_Saraswathy,_Menon_2026.pdf (437,20 KB)
MD5: BD1E2802BEECBEA316C2D5B47966E90E
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| Abstract: | A dominating set S ⊆ V is a co-secure dominating set if for each u ∈ S there exists v ∈ V \ S such that v is adjacent to u and (S \ {u}) ∪ {v} is a dominating set. The cardinality of a minimum co-secure dominating set in G is called the cosecure domination number of G and is denoted by γcs(G). The study of a co-secure dominating set is important in interconnection networks as it studies its security. In cosecure domination, a guard can ensure the safety of only one of its adjacent unguarded vertices. This motivated us to define a new domination parameter called complete co-secure domination, in which a guard can move to any one of its adjacent unguarded vertices without compromising the protection of G. A co-secure dominating set S is called a complete co-secure dominating set if for every u ∈ S and for every v ∈ V \ S that is adjacent to u, (S \ {u})∪ {v} is a dominating set. The cardinality of a minimum complete co-secure dominating set is called the complete co-secure domination number of G and is denoted by γccs(G). In this paper, we study the complete co-secure domination in graphs and determined the lower and upper bounds and have checked their sharpness. We have proved that for any positive integer m, there exists a graph whose co-secure domination number is m and complete co-secure domination number is b, where m ≤ b ≤ 2m. We characterize graphs G such that γcs(G) = γccs(G). We obtain a condition for which γcs(G) = γccs(G) = γs(G) for graphs with δ(G) ≥ 2, thus partially resolving a question posed in paper from Arumugam, Ebadi and Manrique from 2014. We also obtain the complete co-secure domination number of some families of graphs. |
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| Keywords: | domination number, co-secure domination number, complete co-secure domination number |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 08.12.2025 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2026 |
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| Number of pages: | 16 str. |
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| Numbering: | Vol. 9, no. 1, [article no.] P1.09 |
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| PID: | 20.500.12556/RUP-22824  |
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| UDC: | 51 |
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| eISSN: | 2590-9770 |
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| DOI: | 10.26493/2590-9770.1815.df2 |
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| Publication date in RUP: | 20.03.2026 |
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| Views: | 122 |
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| Downloads: | 8 |
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