On graphs with graphic imbalance sequences
The imbalance of the edge e=uv in a graph \(G\) is the value \(imb_{G}(e)=|d_{G}(u)-d_{G}(v)|\). We prove that the sequence \(M_{G}\) of all edge imbalances in \(G\) is graphic for several classes of graphs including trees, graphs in which all non-leaf vertices form a clique and the so-called comple...
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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1049 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-10492018-04-26T02:28:53Z On graphs with graphic imbalance sequences Kozerenko, Sergiy Skochko, Volodymyr edge imbalance, graph irregularity, graphic sequence 05C07, 05C99 The imbalance of the edge e=uv in a graph \(G\) is the value \(imb_{G}(e)=|d_{G}(u)-d_{G}(v)|\). We prove that the sequence \(M_{G}\) of all edge imbalances in \(G\) is graphic for several classes of graphs including trees, graphs in which all non-leaf vertices form a clique and the so-called complete extensions of paths, cycles and complete graphs. Also, we formulate two interesting conjectures related to graphicality of \(M_{G}\). Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1049 Algebra and Discrete Mathematics; Vol 18, No 1 (2014) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1049/571 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
edge imbalance graph irregularity graphic sequence 05C07 05C99 |
| spellingShingle |
edge imbalance graph irregularity graphic sequence 05C07 05C99 Kozerenko, Sergiy Skochko, Volodymyr On graphs with graphic imbalance sequences |
| topic_facet |
edge imbalance graph irregularity graphic sequence 05C07 05C99 |
| format |
Article |
| author |
Kozerenko, Sergiy Skochko, Volodymyr |
| author_facet |
Kozerenko, Sergiy Skochko, Volodymyr |
| author_sort |
Kozerenko, Sergiy |
| title |
On graphs with graphic imbalance sequences |
| title_short |
On graphs with graphic imbalance sequences |
| title_full |
On graphs with graphic imbalance sequences |
| title_fullStr |
On graphs with graphic imbalance sequences |
| title_full_unstemmed |
On graphs with graphic imbalance sequences |
| title_sort |
on graphs with graphic imbalance sequences |
| description |
The imbalance of the edge e=uv in a graph \(G\) is the value \(imb_{G}(e)=|d_{G}(u)-d_{G}(v)|\). We prove that the sequence \(M_{G}\) of all edge imbalances in \(G\) is graphic for several classes of graphs including trees, graphs in which all non-leaf vertices form a clique and the so-called complete extensions of paths, cycles and complete graphs. Also, we formulate two interesting conjectures related to graphicality of \(M_{G}\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1049 |
| work_keys_str_mv |
AT kozerenkosergiy ongraphswithgraphicimbalancesequences AT skochkovolodymyr ongraphswithgraphicimbalancesequences |
| first_indexed |
2024-04-12T06:25:33Z |
| last_indexed |
2024-04-12T06:25:33Z |
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1796109204802502656 |