{"title":"图形的强积和词积的欧米茄指数","authors":"M. Huilgol, Grace Divya D'Souza, I. N. Cangul","doi":"10.2174/0115701794281945240327053046","DOIUrl":null,"url":null,"abstract":"\n\nThe degree sequence of a graph is the list of its vertex degrees arranged in usually increasing order. Many properties of the graphs realized from a degree sequence can be deduced by means of a recently introduced graph invariant called omega invariant.\n\n\n\nWe used the definitions of the considered graph products together with the list of de-gree sequences of these graph products for some well-know graph classes. Naturally, the vertex degree and edge degree partitions are used. As the main theme of the paper is the omega invari-ant, we frequently used the definition and fundamental properties of this very new invariant for our calculations. Also, some algebraic properties of these products are deduced in line with some recent publications following the same fashion\n\n\n\nIn this paper, we determine the degree sequences of strong and lexicographic products of two graphs and obtain the general form of the degree sequences of both products. We obtain a general formula for the omega invariant of strong and lexicographic products of two graphs. The algebraic structures of strong and lexicographic products are obtained. Moreover, we prove that strong and lexicographic products are not distributive over each other\n\n\n\nWe have obtained the general expression for degree sequences of two important products of graphs and a general expression for omega invariants of strong and lexicographic products. Furthermore, we have obtained algebraic structures of strong and lexicographic prod-ucts in terms of their degree sequences. Also, it has been found that the disruptive property does not hold for strong and lexicographic products.\n","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":" 36","pages":""},"PeriodicalIF":16.4000,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Omega Indices of Strong and Lexicographic Products of Graphs\",\"authors\":\"M. Huilgol, Grace Divya D'Souza, I. N. Cangul\",\"doi\":\"10.2174/0115701794281945240327053046\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n\\nThe degree sequence of a graph is the list of its vertex degrees arranged in usually increasing order. Many properties of the graphs realized from a degree sequence can be deduced by means of a recently introduced graph invariant called omega invariant.\\n\\n\\n\\nWe used the definitions of the considered graph products together with the list of de-gree sequences of these graph products for some well-know graph classes. Naturally, the vertex degree and edge degree partitions are used. As the main theme of the paper is the omega invari-ant, we frequently used the definition and fundamental properties of this very new invariant for our calculations. Also, some algebraic properties of these products are deduced in line with some recent publications following the same fashion\\n\\n\\n\\nIn this paper, we determine the degree sequences of strong and lexicographic products of two graphs and obtain the general form of the degree sequences of both products. We obtain a general formula for the omega invariant of strong and lexicographic products of two graphs. The algebraic structures of strong and lexicographic products are obtained. Moreover, we prove that strong and lexicographic products are not distributive over each other\\n\\n\\n\\nWe have obtained the general expression for degree sequences of two important products of graphs and a general expression for omega invariants of strong and lexicographic products. Furthermore, we have obtained algebraic structures of strong and lexicographic prod-ucts in terms of their degree sequences. Also, it has been found that the disruptive property does not hold for strong and lexicographic products.\\n\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":\" 36\",\"pages\":\"\"},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-04-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"92\",\"ListUrlMain\":\"https://doi.org/10.2174/0115701794281945240327053046\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"92","ListUrlMain":"https://doi.org/10.2174/0115701794281945240327053046","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Omega Indices of Strong and Lexicographic Products of Graphs
The degree sequence of a graph is the list of its vertex degrees arranged in usually increasing order. Many properties of the graphs realized from a degree sequence can be deduced by means of a recently introduced graph invariant called omega invariant.
We used the definitions of the considered graph products together with the list of de-gree sequences of these graph products for some well-know graph classes. Naturally, the vertex degree and edge degree partitions are used. As the main theme of the paper is the omega invari-ant, we frequently used the definition and fundamental properties of this very new invariant for our calculations. Also, some algebraic properties of these products are deduced in line with some recent publications following the same fashion
In this paper, we determine the degree sequences of strong and lexicographic products of two graphs and obtain the general form of the degree sequences of both products. We obtain a general formula for the omega invariant of strong and lexicographic products of two graphs. The algebraic structures of strong and lexicographic products are obtained. Moreover, we prove that strong and lexicographic products are not distributive over each other
We have obtained the general expression for degree sequences of two important products of graphs and a general expression for omega invariants of strong and lexicographic products. Furthermore, we have obtained algebraic structures of strong and lexicographic prod-ucts in terms of their degree sequences. Also, it has been found that the disruptive property does not hold for strong and lexicographic products.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.