| Title: | A note on domination and independence-domination numbers of graphs |
|---|
| Authors: | ID Milanič, Martin (Author) |
|---|
| Files: |  RAZ_Milanic_Martin_i2013.pdf (300,57 KB)
MD5: 653E076C3F1DE2F04B4C14DB3DD5D0BA
|
|---|
| Language: | English |
|---|
| Work type: | Unknown |
|---|
| Typology: | 1.08 - Published Scientific Conference Contribution |
|---|
| Organization: | ZUP - University of Primorska Press
|
|---|
| Abstract: | Vizing's conjecture is true for graphs ▫$G$▫ satisfying ▫$\gamma^i(G) = \gamma(G)$▫, where ▫$\gamma(G)$▫ is the domination number of a graph ▫$G$▫ and ▫$\gamma^i(G)$▫ is the independence-domination number of ▫$G$▫, that is, the maximum, over all independent sets ▫$I$▫ in ▫$G$▫, of the minimum number of vertices needed to dominate ▫$I$▫. The equality ▫$\gamma^i(G) = \gamma(G)$▫ is known to hold for all chordal graphs and for chordless cycles of length ▫$0 \pmod{3}$▫. We prove some results related to graphs for which the above equality holds. More specifically, we show that the problems of determining whether ▫$\gamma^i(G) = \gamma(G) = 2$▫ and of verifying whether ▫$\gamma^i(G) \ge 2$▫ are NP-complete, even if ▫$G$▫ is weakly chordal. We also initiate the study of the equality ▫$\gamma^i = \gamma$▫ in the context of hereditary graph classes and exhibit two infinite families of graphs for which ▫$\gamma^i < \gamma$▫. |
|---|
| Keywords: | Vizing's conjecture, domination number, independence-domination number, weakly chordal graph, NP-completeness, hereditary graph class, IDD-perfect graph |
|---|
| Year of publishing: | 2013 |
|---|
| Number of pages: | str. 89-97 |
|---|
| Numbering: | Vol. 6, no. 1 |
|---|
| PID: | 20.500.12556/RUP-2624  |
|---|
| UDC: | 519.17 |
|---|
| ISSN on article: | 1855-3966 |
|---|
| COBISS.SI-ID: | 1024423764 |
|---|
| Publication date in RUP: | 15.10.2013 |
|---|
| Views: | 3082 |
|---|
| Downloads: | 128 |
|---|
| Metadata: |     |
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
