Total Partial Domination in Graphs Under Some Binary Operations
| Autor: | Rowena T. Isla, Roselainie Dimasindil Macapodi |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Vertex (graph theory) Numerical Analysis Algebra and Number Theory Simple graph Domination analysis Applied Mathematics Cartesian product Lexicographical order Theoretical Computer Science Combinatorics symbols.namesake Binary operation Dominating set symbols Geometry and Topology Mathematics |
| Zdroj: | European Journal of Pure and Applied Mathematics. 12:1643-1655 |
| ISSN: | 1307-5543 |
| DOI: | 10.29020/nybg.ejpam.v12i4.3554 |
| Popis: | Let G = (V (G), E(G)) be a simple graph and let α ∈ (0, 1]. A set S ⊆ V (G) isan α-partial dominating set in G if |N[S]| ≥ α |V (G)|. The smallest cardinality of an α-partialdominating set in G is called the α-partial domination number of G, denoted by ∂α(G). An α-partial dominating set S ⊆ V (G) is a total α-partial dominating set in G if every vertex in S isadjacent to some vertex in S. The total α-partial domination number of G, denoted by ∂T α(G), isthe smallest cardinality of a total α-partial dominating set in G. In this paper, we characterize thetotal partial dominating sets in the join, corona, lexicographic and Cartesian products of graphsand determine the exact values or sharp bounds of the corresponding total partial dominationnumber of these graphs. |
| Databáze: | OpenAIRE |
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