International Journal of Mathematics Trends and Technology
Volume 70 | Issue 5 | Year 2024 | Article Id. IJMTT-V70I5P102 | DOI : https://doi.org/10.14445/22315373/IJMTT-V70I5P102
| Received | Revised | Accepted | Published |
|---|---|---|---|
| 20 Mar 2024 | 25 Apr 2024 | 13 May 2024 | 26 May 2024 |
Consider a graph ๐บ(๐, ๐ธ) and a dominating set ๐ท๐, the degree of a dominating set ๐ท๐ is the sum of the degree of
all the vertices in ๐ท๐ and is written as ๐๐๐(๐ท๐). The degree of the set is the sum of the degrees of all the vertices of the set.
The minimum degree among all the dominating sets is called the degree dominating set and is written as ๐ท๐
. Now, a
dominating set ๐ท๐
is an accurate degree dominating set if ๐ โ ๐ท๐ has no degree dominating set of the cardinality of ๐ท๐
. The
accurate degree domination number ๐พ๐
ยฐ
(๐บ) of a given graph ๐บ is the minimum number of vertices in an accurate degree
dominating set of ๐บ. This paper initiates the study of an accurate degree domination number ๐ค๐
ยฐ
(๐บ). Further, obtain some
bounds for ๐พ๐
ยฐ
(๐บ), and the numerical value of ๐พ๐
ยฐ
(๐บ) some standard graphs like path, cycle, wheel, complete graph,
complete bipartite graph.
Dominating set, Degree dominating set, Accurate dominating set, Accurate degree dominating set.
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Moumita K. Chatterjee, Mallikarjun B. Kattimani, Pavitra P. Kumbargoudra, "The Accurate Degree Domination Number of a Graph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 70, no. 5, pp. 9-12, 2024. Crossref, https://doi.org/10.14445/22315373/IJMTT-V70I5P102
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