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...
Збережено в:
| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1049 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | 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 \(M_{G}\). |
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