Distinguishing index of Kronecker product of two graphs
<p class="p1">The distinguishing index <em>D'</em>(<em>G</em>)<span class="Apple-converted-space"> </span>of a graph <em>G</em> is the least integer <em>d</em> such that <em>G</em> has an edge lab...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia
2021-04-01
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| Series: | Electronic Journal of Graph Theory and Applications |
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| Online Access: | https://www.ejgta.org/index.php/ejgta/article/view/338 |
| _version_ | 1811335760211607552 |
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| author | Saeid Alikhani Samaneh Soltani |
| author_facet | Saeid Alikhani Samaneh Soltani |
| author_sort | Saeid Alikhani |
| collection | DOAJ |
| description | <p class="p1">The distinguishing index <em>D'</em>(<em>G</em>)<span class="Apple-converted-space"> </span>of a graph <em>G</em> is the least integer <em>d</em> such that <em>G</em> has an edge labeling<span class="Apple-converted-space"> </span>with <em>d</em> labels<span class="Apple-converted-space"> </span>that is preserved only by a trivial automorphism. The Kronecker product <em>G x H</em> of two graphs <em>G</em> and <em>H</em> is the graph with vertex set <em>V</em>(<em>G</em>) <em>x</em> <em>V</em>(<em>H</em>) and edge set {{(<em>u,x</em>), (<em>v,y</em>)} |{<em>u,v</em>} ∈ <em>E</em>(<em>G</em>) and {<em>x</em>,<em>y</em>} ∈<span class="Apple-converted-space"> </span><em>E</em>(<em>H</em>)}. In this paper we study the<span class="Apple-converted-space"> </span>distinguishing index of Kronecker product of two graphs.<span class="Apple-converted-space"> </span></p> |
| first_indexed | 2024-04-13T17:29:48Z |
| format | Article |
| id | doaj.art-a5f4d263b3d0485896f530ad03615474 |
| institution | Directory Open Access Journal |
| issn | 2338-2287 |
| language | English |
| last_indexed | 2024-04-13T17:29:48Z |
| publishDate | 2021-04-01 |
| publisher | Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia |
| record_format | Article |
| series | Electronic Journal of Graph Theory and Applications |
| spelling | doaj.art-a5f4d263b3d0485896f530ad036154742022-12-22T02:37:37ZengIndonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), IndonesiaElectronic Journal of Graph Theory and Applications2338-22872021-04-0191778510.5614//ejgta.2021.9.1.7203Distinguishing index of Kronecker product of two graphsSaeid Alikhani0Samaneh Soltani1Department of Mathematics, Yazd University, 89195-741, Yazd, IranDepartment of Mathematics, Yazd University, 89195-741, Yazd, Iran<p class="p1">The distinguishing index <em>D'</em>(<em>G</em>)<span class="Apple-converted-space"> </span>of a graph <em>G</em> is the least integer <em>d</em> such that <em>G</em> has an edge labeling<span class="Apple-converted-space"> </span>with <em>d</em> labels<span class="Apple-converted-space"> </span>that is preserved only by a trivial automorphism. The Kronecker product <em>G x H</em> of two graphs <em>G</em> and <em>H</em> is the graph with vertex set <em>V</em>(<em>G</em>) <em>x</em> <em>V</em>(<em>H</em>) and edge set {{(<em>u,x</em>), (<em>v,y</em>)} |{<em>u,v</em>} ∈ <em>E</em>(<em>G</em>) and {<em>x</em>,<em>y</em>} ∈<span class="Apple-converted-space"> </span><em>E</em>(<em>H</em>)}. In this paper we study the<span class="Apple-converted-space"> </span>distinguishing index of Kronecker product of two graphs.<span class="Apple-converted-space"> </span></p>https://www.ejgta.org/index.php/ejgta/article/view/338distinguishing number, distinguishing index, kronecker product |
| spellingShingle | Saeid Alikhani Samaneh Soltani Distinguishing index of Kronecker product of two graphs Electronic Journal of Graph Theory and Applications distinguishing number, distinguishing index, kronecker product |
| title | Distinguishing index of Kronecker product of two graphs |
| title_full | Distinguishing index of Kronecker product of two graphs |
| title_fullStr | Distinguishing index of Kronecker product of two graphs |
| title_full_unstemmed | Distinguishing index of Kronecker product of two graphs |
| title_short | Distinguishing index of Kronecker product of two graphs |
| title_sort | distinguishing index of kronecker product of two graphs |
| topic | distinguishing number, distinguishing index, kronecker product |
| url | https://www.ejgta.org/index.php/ejgta/article/view/338 |
| work_keys_str_mv | AT saeidalikhani distinguishingindexofkroneckerproductoftwographs AT samanehsoltani distinguishingindexofkroneckerproductoftwographs |