{"title":"k图的拓扑指标","authors":"Ahmed Ayache , Abdu Alameri","doi":"10.1016/j.jaubas.2017.03.001","DOIUrl":null,"url":null,"abstract":"<div><p>This paper is devoted to the study of a new graph, called <span><math><mrow><msup><mrow><mi>m</mi></mrow><mrow><mi>k</mi></mrow></msup></mrow></math></span>-graph and denoted by <span><math><mrow><msup><mrow><mi>m</mi></mrow><mrow><mi>k</mi></mrow></msup><mo>(</mo><mi>G</mi><mo>)</mo></mrow></math></span>, that arises from a simple graph <em>G</em> by <em>k</em> successive iterations of a special kind of construction. We provide some of its topological indices such as Wiener index, Hyper-Wiener index, Wiener polarity, Zagreb indices, Schultz and modified Schultz indices and Wiener-type invariant. Some Formulas concerning classical graphs are settled to show the scope of this study.</p></div>","PeriodicalId":17232,"journal":{"name":"Journal of the Association of Arab Universities for Basic and Applied Sciences","volume":"24 ","pages":"Pages 283-291"},"PeriodicalIF":0.0000,"publicationDate":"2017-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jaubas.2017.03.001","citationCount":"10","resultStr":"{\"title\":\"Topological indices of the mk-graph\",\"authors\":\"Ahmed Ayache , Abdu Alameri\",\"doi\":\"10.1016/j.jaubas.2017.03.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper is devoted to the study of a new graph, called <span><math><mrow><msup><mrow><mi>m</mi></mrow><mrow><mi>k</mi></mrow></msup></mrow></math></span>-graph and denoted by <span><math><mrow><msup><mrow><mi>m</mi></mrow><mrow><mi>k</mi></mrow></msup><mo>(</mo><mi>G</mi><mo>)</mo></mrow></math></span>, that arises from a simple graph <em>G</em> by <em>k</em> successive iterations of a special kind of construction. We provide some of its topological indices such as Wiener index, Hyper-Wiener index, Wiener polarity, Zagreb indices, Schultz and modified Schultz indices and Wiener-type invariant. Some Formulas concerning classical graphs are settled to show the scope of this study.</p></div>\",\"PeriodicalId\":17232,\"journal\":{\"name\":\"Journal of the Association of Arab Universities for Basic and Applied Sciences\",\"volume\":\"24 \",\"pages\":\"Pages 283-291\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.jaubas.2017.03.001\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Association of Arab Universities for Basic and Applied Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1815385217300147\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Association of Arab Universities for Basic and Applied Sciences","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1815385217300147","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper is devoted to the study of a new graph, called -graph and denoted by , that arises from a simple graph G by k successive iterations of a special kind of construction. We provide some of its topological indices such as Wiener index, Hyper-Wiener index, Wiener polarity, Zagreb indices, Schultz and modified Schultz indices and Wiener-type invariant. Some Formulas concerning classical graphs are settled to show the scope of this study.
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