Gui-Xian Tian , Hui-Lu Sun , Shu-Yu Cui , Jun-Xing Wu
{"title":"扰边对两种特殊类型图的塞德尔能的影响","authors":"Gui-Xian Tian , Hui-Lu Sun , Shu-Yu Cui , Jun-Xing Wu","doi":"10.1016/j.kjs.2024.100311","DOIUrl":null,"url":null,"abstract":"<div><p>Let <span><math><mi>G</mi></math></span> be a simple undirected graph, and let <span><math><mrow><mi>S</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> be its Seidel matrix. The Seidel energy of <span><math><mi>G</mi></math></span> is defined as <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>S</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>=</mo><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mrow><mo>|</mo><msub><mrow><mi>λ</mi></mrow><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>|</mo></mrow></mrow></math></span>, where <span><math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>,</mo><msub><mrow><mi>λ</mi></mrow><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>λ</mi></mrow><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> are Seidel eigenvalues of <span><math><mi>G</mi></math></span>. Recently, researchers have studied the effect of embedded edges on the distance energy of complete bipartite graphs. In this paper, the effect of perturbed edges on the Seidel energy of complete bipartite graphs and complete split graphs is studied. Finally, these graphs are ordered according to their Seidal energies.</p></div>","PeriodicalId":17848,"journal":{"name":"Kuwait Journal of Science","volume":"52 1","pages":"Article 100311"},"PeriodicalIF":1.2000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2307410824001366/pdfft?md5=21ca43aba48460704d798ad7853a4947&pid=1-s2.0-S2307410824001366-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Effects on Seidel energy of two special types of graphs by perturbing edges\",\"authors\":\"Gui-Xian Tian , Hui-Lu Sun , Shu-Yu Cui , Jun-Xing Wu\",\"doi\":\"10.1016/j.kjs.2024.100311\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <span><math><mi>G</mi></math></span> be a simple undirected graph, and let <span><math><mrow><mi>S</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> be its Seidel matrix. The Seidel energy of <span><math><mi>G</mi></math></span> is defined as <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>S</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>=</mo><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><mrow><mo>|</mo><msub><mrow><mi>λ</mi></mrow><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>|</mo></mrow></mrow></math></span>, where <span><math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>,</mo><msub><mrow><mi>λ</mi></mrow><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>λ</mi></mrow><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> are Seidel eigenvalues of <span><math><mi>G</mi></math></span>. Recently, researchers have studied the effect of embedded edges on the distance energy of complete bipartite graphs. In this paper, the effect of perturbed edges on the Seidel energy of complete bipartite graphs and complete split graphs is studied. Finally, these graphs are ordered according to their Seidal energies.</p></div>\",\"PeriodicalId\":17848,\"journal\":{\"name\":\"Kuwait Journal of Science\",\"volume\":\"52 1\",\"pages\":\"Article 100311\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-08-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S2307410824001366/pdfft?md5=21ca43aba48460704d798ad7853a4947&pid=1-s2.0-S2307410824001366-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Kuwait Journal of Science\",\"FirstCategoryId\":\"103\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2307410824001366\",\"RegionNum\":4,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kuwait Journal of Science","FirstCategoryId":"103","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2307410824001366","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0
摘要
设 G 是一个简单的无向图,S(G) 是它的塞德尔矩阵。G 的 Seidel 能量定义为 ES(G)=∑i=1n|λSi(G)| 其中,λS1(G),λS2(G),...,λSn(G) 是 G 的 Seidel 特征值。最近,研究人员研究了嵌入边对完整双向图距离能量的影响。本文研究了扰动边对完整双方图和完整分裂图的 Seidel 能量的影响。最后,根据这些图的塞德尔能对它们进行了排序。
Effects on Seidel energy of two special types of graphs by perturbing edges
Let be a simple undirected graph, and let be its Seidel matrix. The Seidel energy of is defined as , where are Seidel eigenvalues of . Recently, researchers have studied the effect of embedded edges on the distance energy of complete bipartite graphs. In this paper, the effect of perturbed edges on the Seidel energy of complete bipartite graphs and complete split graphs is studied. Finally, these graphs are ordered according to their Seidal energies.
期刊介绍:
Kuwait Journal of Science (KJS) is indexed and abstracted by major publishing houses such as Chemical Abstract, Science Citation Index, Current contents, Mathematics Abstract, Micribiological Abstracts etc. KJS publishes peer-review articles in various fields of Science including Mathematics, Computer Science, Physics, Statistics, Biology, Chemistry and Earth & Environmental Sciences. In addition, it also aims to bring the results of scientific research carried out under a variety of intellectual traditions and organizations to the attention of specialized scholarly readership. As such, the publisher expects the submission of original manuscripts which contain analysis and solutions about important theoretical, empirical and normative issues.