| Autor: |
Selvi, V., Sujin Flower, V. |
| Předmět: |
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| Zdroj: |
Discrete Mathematics, Algorithms & Applications; Feb2024, Vol. 16 Issue 2, p1-17, 17p |
| Abstrakt: |
Let G be a connected graph and S be a minimum geodetic global dominating set of G. A subset T ⊆ S is called a forcing subset for S if S is the unique minimum geodetic global dominating set containing T. A forcing subset for S of minimum cardinality is a minimum forcing subset of S. The forcing geodetic global domination number of S , denoted by f γ ¯ g (S) , is the cardinality of a minimum forcing subset of S. The forcing geodetic global domination number of G , denoted by f γ ¯ g (G) , is f γ ¯ g (G) = min { f γ ¯ g (S) } , where the minimum is taken over all minimum geodetic global dominating sets S in G. The forcing geodetic global domination number of some standard graphs are determined. Some of its general properties are studied. It is shown that for every pair of positive integers a and b with 0 ≤ a ≤ b and b > a + 2 , there exists a connected graph G such that f γ ¯ g (G) = a and γ ¯ (G) = b. The geodetic global domination number of join of graphs is also studied. Connected graphs of order n ≥ 2 with geodetic global domination number 2 are characterized. It is proved that, for a connected graph G with γ ¯ g (G) = 2. Then 0 ≤ f γ ¯ g (G) ≤ 1 and characterized connected graphs for which the lower and the upper bounds are sharp. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
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