{"title":"边缘删除导致的 ISI 能量变化","authors":"Ahmad Bilal, Muhammad Mobeen Munir","doi":"10.1002/qua.27501","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>The problem of characterization of all graphs where the deletion of an edge results in decrease or increase in the energy is far from completion. To be more exact, we solve this problem for Inverse Sum Indeg energy. We compute the ISI energies of edge deleted graphs of <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mrow>\n <mi>K</mi>\n </mrow>\n <mrow>\n <mi>n</mi>\n </mrow>\n </msub>\n </mrow>\n <annotation>$$ {K}_n $$</annotation>\n </semantics></math>, <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mrow>\n <mi>K</mi>\n </mrow>\n <mrow>\n <mi>n</mi>\n <mo>,</mo>\n <mi>n</mi>\n </mrow>\n </msub>\n </mrow>\n <annotation>$$ {K}_{n,n} $$</annotation>\n </semantics></math>, <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mrow>\n <mi>K</mi>\n </mrow>\n <mrow>\n <mi>n</mi>\n <mo>,</mo>\n <mi>n</mi>\n <mo>,</mo>\n <mi>n</mi>\n </mrow>\n </msub>\n </mrow>\n <annotation>$$ {K}_{n,n,n} $$</annotation>\n </semantics></math>, and star graph, finally we compare the respective energies from the original graphs. We give different graphs where both cases can happen. This serves as partial solutions of the modified version of the hard to crack problem posed by Gutman to characterize all graphs whose energy decreases after deletion of an edge.</p>\n </div>","PeriodicalId":182,"journal":{"name":"International Journal of Quantum Chemistry","volume":"124 22","pages":""},"PeriodicalIF":2.3000,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ISI Energy Change Due to an Edge Deletion\",\"authors\":\"Ahmad Bilal, Muhammad Mobeen Munir\",\"doi\":\"10.1002/qua.27501\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n \\n <p>The problem of characterization of all graphs where the deletion of an edge results in decrease or increase in the energy is far from completion. To be more exact, we solve this problem for Inverse Sum Indeg energy. We compute the ISI energies of edge deleted graphs of <span></span><math>\\n <semantics>\\n <mrow>\\n <msub>\\n <mrow>\\n <mi>K</mi>\\n </mrow>\\n <mrow>\\n <mi>n</mi>\\n </mrow>\\n </msub>\\n </mrow>\\n <annotation>$$ {K}_n $$</annotation>\\n </semantics></math>, <span></span><math>\\n <semantics>\\n <mrow>\\n <msub>\\n <mrow>\\n <mi>K</mi>\\n </mrow>\\n <mrow>\\n <mi>n</mi>\\n <mo>,</mo>\\n <mi>n</mi>\\n </mrow>\\n </msub>\\n </mrow>\\n <annotation>$$ {K}_{n,n} $$</annotation>\\n </semantics></math>, <span></span><math>\\n <semantics>\\n <mrow>\\n <msub>\\n <mrow>\\n <mi>K</mi>\\n </mrow>\\n <mrow>\\n <mi>n</mi>\\n <mo>,</mo>\\n <mi>n</mi>\\n <mo>,</mo>\\n <mi>n</mi>\\n </mrow>\\n </msub>\\n </mrow>\\n <annotation>$$ {K}_{n,n,n} $$</annotation>\\n </semantics></math>, and star graph, finally we compare the respective energies from the original graphs. We give different graphs where both cases can happen. This serves as partial solutions of the modified version of the hard to crack problem posed by Gutman to characterize all graphs whose energy decreases after deletion of an edge.</p>\\n </div>\",\"PeriodicalId\":182,\"journal\":{\"name\":\"International Journal of Quantum Chemistry\",\"volume\":\"124 22\",\"pages\":\"\"},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2024-11-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Quantum Chemistry\",\"FirstCategoryId\":\"92\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/qua.27501\",\"RegionNum\":3,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"CHEMISTRY, PHYSICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Quantum Chemistry","FirstCategoryId":"92","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/qua.27501","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0
摘要
对于删除一条边会导致能量减少或增加的所有图形的特征描述问题，我们还远远没有完成。更确切地说，我们要解决的是反相加能量（Inverse Sum Indeg energy）问题。我们计算了 K n $$ {K}_n $$ , K n , n $$ {K}_{n,n} $$ , K n , n , n $$ {K}_{n,n,n} $$ 和星形图中删除边的 ISI 能量，最后比较了原始图中各自的能量。我们给出了两种情况都可能发生的不同图形。这可以作为古特曼提出的难以破解问题的修正版的部分解决方案，以描述删除一条边后能量会降低的所有图的特征。
The problem of characterization of all graphs where the deletion of an edge results in decrease or increase in the energy is far from completion. To be more exact, we solve this problem for Inverse Sum Indeg energy. We compute the ISI energies of edge deleted graphs of , , , and star graph, finally we compare the respective energies from the original graphs. We give different graphs where both cases can happen. This serves as partial solutions of the modified version of the hard to crack problem posed by Gutman to characterize all graphs whose energy decreases after deletion of an edge.
期刊介绍：
Since its first formulation quantum chemistry has provided the conceptual and terminological framework necessary to understand atoms, molecules and the condensed matter. Over the past decades synergistic advances in the methodological developments, software and hardware have transformed quantum chemistry in a truly interdisciplinary science that has expanded beyond its traditional core of molecular sciences to fields as diverse as chemistry and catalysis, biophysics, nanotechnology and material science.
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