On inclusive distance vertex irregular labelings
<p>For a simple graph <span class="math"><em>G</em></span>, a vertex labeling <span class="math"><em>f</em> : <em>V</em>(<em>G</em>) → {1, 2, ..., <em>k</em>}</span> is called a <span cla...
| 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
2018-04-01
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| Series: | Electronic Journal of Graph Theory and Applications |
| Subjects: | |
| Online Access: | https://www.ejgta.org/index.php/ejgta/article/view/463 |
| _version_ | 1818469903219294208 |
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| author | Martin Baca Andrea Semanicova-Fenovcikova S. Slamin Kiki A. Sugeng |
| author_facet | Martin Baca Andrea Semanicova-Fenovcikova S. Slamin Kiki A. Sugeng |
| author_sort | Martin Baca |
| collection | DOAJ |
| description | <p>For a simple graph <span class="math"><em>G</em></span>, a vertex labeling <span class="math"><em>f</em> : <em>V</em>(<em>G</em>) → {1, 2, ..., <em>k</em>}</span> is called a <span class="math"><em>k</em></span>-labeling. The weight of a vertex <span class="math"><em>v</em></span>, denoted by <span class="math"><em>w</em><em>t</em><sub><em>f</em></sub>(<em>v</em>)</span> is the sum of all vertex labels of vertices in the closed neighborhood of the vertex <span class="math"><em>v</em></span>. A vertex <span class="math"><em>k</em></span>-labeling is defined to be an inclusive distance vertex irregular distance <span class="math"><em>k</em></span>-labeling of <span class="math"><em>G</em></span> if for every two different vertices <span class="math"><em>u</em></span> and <span class="math"><em>v</em></span> there is <span class="math"><em>w</em><em>t</em><sub><em>f</em></sub>(<em>u</em>) ≠ <em>w</em><em>t</em><sub><em>f</em></sub>(<em>v</em>)</span>. The minimum <span class="math"><em>k</em></span> for which the graph <span class="math"><em>G</em></span> has a vertex irregular distance <span class="math"><em>k</em></span>-labeling is called the inclusive distance vertex irregularity strength of <span class="math"><em>G</em></span>. In this paper we establish a lower bound of the inclusive distance vertex irregularity strength for any graph and determine the exact value of this parameter for several families of graphs.</p> |
| first_indexed | 2024-04-13T21:30:52Z |
| format | Article |
| id | doaj.art-a0e3c7909b7e4f6fa4d7ad55c33e4d62 |
| institution | Directory Open Access Journal |
| issn | 2338-2287 |
| language | English |
| last_indexed | 2024-04-13T21:30:52Z |
| publishDate | 2018-04-01 |
| 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-a0e3c7909b7e4f6fa4d7ad55c33e4d622022-12-22T02:29:10ZengIndonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), IndonesiaElectronic Journal of Graph Theory and Applications2338-22872018-04-0161618310.5614/ejgta.2018.6.1.5106On inclusive distance vertex irregular labelingsMartin Baca0Andrea Semanicova-Fenovcikova1S. Slamin2Kiki A. Sugeng3Department of Applied Mathematics and Informatics, Technical University, Letna 9, Kosice, SlovakiaDepartment of Applied Mathematics and Informatics, Technical University, Letna 9, Kosice, SlovakiaInformation System Study Program, University of Jember, Jl. Kalimantan 37 Jember, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Kampus UI Depok, Depok 16424, Indonesia<p>For a simple graph <span class="math"><em>G</em></span>, a vertex labeling <span class="math"><em>f</em> : <em>V</em>(<em>G</em>) → {1, 2, ..., <em>k</em>}</span> is called a <span class="math"><em>k</em></span>-labeling. The weight of a vertex <span class="math"><em>v</em></span>, denoted by <span class="math"><em>w</em><em>t</em><sub><em>f</em></sub>(<em>v</em>)</span> is the sum of all vertex labels of vertices in the closed neighborhood of the vertex <span class="math"><em>v</em></span>. A vertex <span class="math"><em>k</em></span>-labeling is defined to be an inclusive distance vertex irregular distance <span class="math"><em>k</em></span>-labeling of <span class="math"><em>G</em></span> if for every two different vertices <span class="math"><em>u</em></span> and <span class="math"><em>v</em></span> there is <span class="math"><em>w</em><em>t</em><sub><em>f</em></sub>(<em>u</em>) ≠ <em>w</em><em>t</em><sub><em>f</em></sub>(<em>v</em>)</span>. The minimum <span class="math"><em>k</em></span> for which the graph <span class="math"><em>G</em></span> has a vertex irregular distance <span class="math"><em>k</em></span>-labeling is called the inclusive distance vertex irregularity strength of <span class="math"><em>G</em></span>. In this paper we establish a lower bound of the inclusive distance vertex irregularity strength for any graph and determine the exact value of this parameter for several families of graphs.</p>https://www.ejgta.org/index.php/ejgta/article/view/463inclusive distance vertex irregular labeling, inclusive distance vertex irregularity strength |
| spellingShingle | Martin Baca Andrea Semanicova-Fenovcikova S. Slamin Kiki A. Sugeng On inclusive distance vertex irregular labelings Electronic Journal of Graph Theory and Applications inclusive distance vertex irregular labeling, inclusive distance vertex irregularity strength |
| title | On inclusive distance vertex irregular labelings |
| title_full | On inclusive distance vertex irregular labelings |
| title_fullStr | On inclusive distance vertex irregular labelings |
| title_full_unstemmed | On inclusive distance vertex irregular labelings |
| title_short | On inclusive distance vertex irregular labelings |
| title_sort | on inclusive distance vertex irregular labelings |
| topic | inclusive distance vertex irregular labeling, inclusive distance vertex irregularity strength |
| url | https://www.ejgta.org/index.php/ejgta/article/view/463 |
| work_keys_str_mv | AT martinbaca oninclusivedistancevertexirregularlabelings AT andreasemanicovafenovcikova oninclusivedistancevertexirregularlabelings AT sslamin oninclusivedistancevertexirregularlabelings AT kikiasugeng oninclusivedistancevertexirregularlabelings |