Pub Date : 2018-06-01DOI: 10.52737/18291163-2018.10.2-1-11
M. Alaeiyan, A. Mehrabani
Perfect coloring is a generalization of the notion of completely regular codes, given by Delsarte. A perfect $m$-coloring of a graph $G$ with $m$ colors is a partition of the vertex set of $G$ into m parts $A_1$, $dots$, $A_m$ such that, for all $ i,jin lbrace 1,cdots ,mrbrace $, every vertex of $A_i$ is adjacent to the same number of vertices, namely, $a_{ij}$ vertices, of $A_j$ . The matrix $A=(a_{ij})_{i,jin lbrace 1,cdots ,mrbrace }$ is called the parameter matrix. We study the perfect 3-colorings (also known as the equitable partitions into three parts) of the cubic graphs of order $8$. In particular, we classify all the realizable parameter matrices of perfect 3-colorings for the cubic graphs of order 8.
{"title":"Perfect 3-colorings of Cubic Graphs of Order 8","authors":"M. Alaeiyan, A. Mehrabani","doi":"10.52737/18291163-2018.10.2-1-11","DOIUrl":"https://doi.org/10.52737/18291163-2018.10.2-1-11","url":null,"abstract":"Perfect coloring is a generalization of the notion of completely regular codes, given by Delsarte. A perfect $m$-coloring of a graph $G$ with $m$ colors is a partition of the vertex set of $G$ into m parts $A_1$, $dots$, $A_m$ such that, for all $ i,jin lbrace 1,cdots ,mrbrace $, every vertex of $A_i$ is adjacent to the same number of vertices, namely, $a_{ij}$ vertices, of $A_j$ . The matrix $A=(a_{ij})_{i,jin lbrace 1,cdots ,mrbrace }$ is called the parameter matrix. We study the perfect 3-colorings (also known as the equitable partitions into three parts) of the cubic graphs of order $8$. In particular, we classify all the realizable parameter matrices of perfect 3-colorings for the cubic graphs of order 8.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49345845","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}
Pub Date : 2016-06-01DOI: 10.52737/18291163-2018.10.3-1-10
N. Kehayopulu
Most of the results on semigroups or ordered semigroups can be transferred to hypersemigroups or to ordered hypersemigroups, respectively. The same, if we replace the word "semigroup" by "groupoid", "hypersemigroup" by "hypergroupoid". We show the way we pass from fuzzy ordered semigroups to fuzzy hypersemigroups.
{"title":"Fuzzy Right (Left) Ideals in Hypergroupoids and Fuzzy Bi-ideals in Hypersemigroups","authors":"N. Kehayopulu","doi":"10.52737/18291163-2018.10.3-1-10","DOIUrl":"https://doi.org/10.52737/18291163-2018.10.3-1-10","url":null,"abstract":"Most of the results on semigroups or ordered semigroups can be transferred to hypersemigroups or to ordered hypersemigroups, respectively. The same, if we replace the word \"semigroup\" by \"groupoid\", \"hypersemigroup\" by \"hypergroupoid\". We show the way we pass from fuzzy ordered semigroups to fuzzy hypersemigroups.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70929401","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}
Pub Date : 2016-03-01DOI: 10.52737/18291163-2018.10.8-1-19
S. Dragomir
Some Lebesgue integral inequalities of Jensen type for λ-convex functions defined on real intervals are given.
给出了实区间上λ-凸函数的若干Lebesgue Jensen型积分不等式。
{"title":"Lebesgue Integral Inequalities of Jensen Type for λ-Convex Functions","authors":"S. Dragomir","doi":"10.52737/18291163-2018.10.8-1-19","DOIUrl":"https://doi.org/10.52737/18291163-2018.10.8-1-19","url":null,"abstract":"Some Lebesgue integral inequalities of Jensen type for λ-convex functions defined on real intervals are given.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70929485","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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