{"title":"cataconsed Polyomino系统的全独立集数","authors":"Haizhen Ren, Dong Zhu, Deqing Xu","doi":"10.12783/DTEEES/PEEES2020/35460","DOIUrl":null,"url":null,"abstract":"A catacondensed polyomino system is a chain polyomino system in which the joining of the centers of its adjacent cells forms a tree. Total independent set number is a graph invariant that has been studied extensively in statistical mechanics and mathematical chemistry. In this paper, we introduce a new graph vector at a given edge and get some recurrence relations on the total independent set numbers of the path-like polyomino systems. Based on these relations, the reduction formulas of computing the total independent set number of any catacondensed polyomino system via transfer matrices can be obtained.","PeriodicalId":11369,"journal":{"name":"DEStech Transactions on Environment, Energy and Earth Science","volume":"7 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Total Independent Set Numbers on Catacondensed Polyomino Systems\",\"authors\":\"Haizhen Ren, Dong Zhu, Deqing Xu\",\"doi\":\"10.12783/DTEEES/PEEES2020/35460\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A catacondensed polyomino system is a chain polyomino system in which the joining of the centers of its adjacent cells forms a tree. Total independent set number is a graph invariant that has been studied extensively in statistical mechanics and mathematical chemistry. In this paper, we introduce a new graph vector at a given edge and get some recurrence relations on the total independent set numbers of the path-like polyomino systems. Based on these relations, the reduction formulas of computing the total independent set number of any catacondensed polyomino system via transfer matrices can be obtained.\",\"PeriodicalId\":11369,\"journal\":{\"name\":\"DEStech Transactions on Environment, Energy and Earth Science\",\"volume\":\"7 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-03-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"DEStech Transactions on Environment, Energy and Earth Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12783/DTEEES/PEEES2020/35460\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"DEStech Transactions on Environment, Energy and Earth Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12783/DTEEES/PEEES2020/35460","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Total Independent Set Numbers on Catacondensed Polyomino Systems
A catacondensed polyomino system is a chain polyomino system in which the joining of the centers of its adjacent cells forms a tree. Total independent set number is a graph invariant that has been studied extensively in statistical mechanics and mathematical chemistry. In this paper, we introduce a new graph vector at a given edge and get some recurrence relations on the total independent set numbers of the path-like polyomino systems. Based on these relations, the reduction formulas of computing the total independent set number of any catacondensed polyomino system via transfer matrices can be obtained.
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