Bibliographic Details
| Title: |
CHARACTERIZATION OF GRAPHS WITH EQUAL DOMINATION AND INDEPENDENT DOMINATION NUMBERS. |
| Authors: |
Bara, Zuraida J.1 zuraidabara0268@gmail.com |
| Source: |
Advances & Applications in Discrete Mathematics. Jul2026, Vol. 43 Issue 5, p675-686. 12p. |
| Subjects: |
Dominating set, Independent sets, Graph theory, Paths & cycles in graph theory |
| Abstract: |
Let G be a finite simple graph. The domination number γ(G) is the minimum cardinality of a dominating set, whereas the independent domination number i(G) is the minimum cardinality of a dominating set that is also independent. Since every independent dominating set is a dominating set, γ (G) ≤ l(G) for every graph G. This paper studies the extremal equality case γ (G) = l(G). We give equivalent characterizations in terms of minimum dominating sets, maximal independent sets, and edge-minimal induced subgraphs on γ-sets. We also prove preservation under disjoint union, determine the equality condition for complete multipartite graphs and joins, and give a separate treatment of paths and cycles, for which the two parameters are equal. The results isolate the structural obstruction to equality: every minimum dominating set must contain adjacent vertices precisely when the independent domination number strictly exceeds the domination number. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
