{"title":"Long Dominating Cycles in Graphs","authors":"A. Yongga, Sun Zhi-ren","doi":"10.5281/ZENODO.9278","DOIUrl":"https://doi.org/10.5281/ZENODO.9278","url":null,"abstract":"Let G be a connected graph of order n, and NC2(G) denote min{|N(u)∪N(v)| : dist(u,v) = 2}, where dist(u,v) is the distance between u and v in G. A cycle C in G is called a dominating cycle, if V (G)V (C) is an independent set in G. In this paper, we prove that if G contains a dominating cycle and � ≥ 2, then G contains a dominating cycle of length at least min{n,2NC2(G) −1} and give a family of graphs showing our result is sharp, which proves a conjecture of R. Shen and F. Tian, also related with the cyclic structures of algebraically Smarandache multi-spaces. subscript G of NG(H). We denote by G(S) the subgraph of G induced by any subset S of V (G). For a connected graph G and u, v ∈ V (G), we define the distance between u and v in G, denoted by dist(u, v), as the minimum value of the lengths of all paths joining u and v in G. If G is non-complete, let NC(G) denote min{|N(u, v)| : uv / ∈ E(G)} and NC2(G) denote min{|N(u, v)| : dist(u, v) = 2}; if G is complete, we set NC(G) = n −1 and NC2(G) = n −1. In (2), Broersma and Veldman gave the following result.","PeriodicalId":69261,"journal":{"name":"内蒙古师范大学学报(哲学社会科学版)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2007-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71093647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"ON DEMOCRATIC CENTRALISM","authors":"Ma Decheng","doi":"10.4135/9781608712434.n397","DOIUrl":"https://doi.org/10.4135/9781608712434.n397","url":null,"abstract":"The formation of democratic centralism as a historical outcome under revolutionary struggle is inevitable.Democratic centralism means differently in the eyes of the revolutionary masters.As the fundamental political system of our country,democratic centralism has its superiority,but it has been distorted or has led to some shortcomings in the practical working of the political system.The construction of harmonious society requires the further perfection of democratic centralism.It should be systematic,standardized,open,transparent,balanced and harmonious.","PeriodicalId":69261,"journal":{"name":"内蒙古师范大学学报(哲学社会科学版)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2007-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70653271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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