Bounds on the parameters of non-$L$-borderenergetic graphs
UDC 519.17 We consider graphs such that their Laplacian energy is equivalent to the Laplacian energy of the complete graph of the same order, which is called an $L$-borderenergetic graph. Firstly, we study the graphs with degree sequence consisting of at most three distinct integers and...
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| Datum: | 2023 |
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| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2023
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7243 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512633843613696 |
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| author | Dede, Cahit Maden, Ayşe Dilek Dede, Cahit Maden, Ayşe Dilek |
| author_facet | Dede, Cahit Maden, Ayşe Dilek Dede, Cahit Maden, Ayşe Dilek |
| author_sort | Dede, Cahit |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-06-19T00:34:40Z |
| description | UDC 519.17
We consider graphs such that their Laplacian energy is equivalent to the Laplacian energy of the complete graph of the same order, which is called an $L$-borderenergetic graph. Firstly, we study the graphs with degree sequence consisting of at most three distinct integers and give new bounds for the number of vertices of these graphs to be non-$L$-borderenergetic. Second, by using Koolen–Moulton and McClelland inequalities, we give new bounds for the number of edges of a non-$L$-borderenergetic graph. Third, we use recent bounds given by Milovanovic, et al. on Laplacian energy to get similar conditions for non-$L$-borderenergetic graphs. Our bounds depend only on the degree sequence of a graph, which is much easier than computing the spectrum of the graph. In other words, we developed a faster approach to exclude non-$L$-borderenergetic graphs. |
| doi_str_mv | 10.3842/umzh.v75i9.7243 |
| first_indexed | 2026-03-24T03:31:54Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7243 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:31:54Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-72432024-06-19T00:34:40Z Bounds on the parameters of non-$L$-borderenergetic graphs Bounds on the parameters of non-$L$-borderenergetic graphs Dede, Cahit Maden, Ayşe Dilek Dede, Cahit Maden, Ayşe Dilek Graph energy Laplacian matrix borderenergetic graph Zagreb index graph UDC 519.17 We consider graphs such that their Laplacian energy is equivalent to the Laplacian energy of the complete graph of the same order, which is called an $L$-borderenergetic graph. Firstly, we study the graphs with degree sequence consisting of at most three distinct integers and give new bounds for the number of vertices of these graphs to be non-$L$-borderenergetic. Second, by using Koolen–Moulton and McClelland inequalities, we give new bounds for the number of edges of a non-$L$-borderenergetic graph. Third, we use recent bounds given by Milovanovic, et al. on Laplacian energy to get similar conditions for non-$L$-borderenergetic graphs. Our bounds depend only on the degree sequence of a graph, which is much easier than computing the spectrum of the graph. In other words, we developed a faster approach to exclude non-$L$-borderenergetic graphs. УДК 519.17 Обмеження на параметри не $L$-граничних енергетичних графів  Ми розглядаємо графи, лапласівська енергія яких еквівалентна лапласівській енергії повного графа такого ж порядку, який називається $L$-граничним енергетичним графом. По-перше, ми вивчаємо графи, для яких послідовність степенів складається не більше ніж з трьох різних цілих чисел, і наводимо нові оцінки для кількості вершин цих графів, за яких вони не є $L$-гранично енергетичними.  По-друге, використовуючи нерівності Кулена–Моултона та МакКлелланда, наводимо нові оцінки для кількості ребер не $L$-граничного енергетичного графа. По-третє, використовуємо оцінки, що були нещодавно отримані Міловановичем та ін. для лапласівської енергії, щоб отримати подібні умови для не $L$-граничних енергетичних графів. Наші оцінки залежать лише від послідовності степенів графа, що набагато зручніше, ніж обчислювати спектр графа. Іншими словами, розроблено більш швидкий підхід для вилучення не $L$-граничних енергетичних графів.  Institute of Mathematics, NAS of Ukraine 2023-09-26 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7243 10.3842/umzh.v75i9.7243 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 9 (2023); 1220 - 1236 Український математичний журнал; Том 75 № 9 (2023); 1220 - 1236 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7243/9748 Copyright (c) 2023 Cahit Dede |
| spellingShingle | Dede, Cahit Maden, Ayşe Dilek Dede, Cahit Maden, Ayşe Dilek Bounds on the parameters of non-$L$-borderenergetic graphs |
| title | Bounds on the parameters of non-$L$-borderenergetic graphs |
| title_alt | Bounds on the parameters of non-$L$-borderenergetic graphs |
| title_full | Bounds on the parameters of non-$L$-borderenergetic graphs |
| title_fullStr | Bounds on the parameters of non-$L$-borderenergetic graphs |
| title_full_unstemmed | Bounds on the parameters of non-$L$-borderenergetic graphs |
| title_short | Bounds on the parameters of non-$L$-borderenergetic graphs |
| title_sort | bounds on the parameters of non-$l$-borderenergetic graphs |
| topic_facet | Graph energy Laplacian matrix borderenergetic graph Zagreb index graph |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7243 |
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