河北师范大学学报—

期刊信息

刊名：河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
主办：河北师范大学
ISSN： 1000-5854
CN： 13-1061/N
中国科技核心期刊
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基于几类包含关系构造距离半正则图

贾冬冬¹

刘鸣²

张更生³

(1.河北科技大学理学院,石家庄 050018； 2.石家庄财经商贸学校,石家庄 050800； 3.河北师范大学数学科学学院,石家庄 050024)
DOI： 10.13763/j.cnki.jhebnu.nse.202501013

Constructions of Distance-semiregular Graphs from Several Kinds of Containment Relations

JIA Dongdong¹,LIU Ming²,ZHANG Gengsheng³

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摘要/Abstract

摘要：

距离半正则图是距离正则图的一类推广,具有一定的正则性和对称性.具有二分类 P∪L 的连通二部图称为关于 P 的距离半正则图,如果对于任意一对距离为 i 的顶点 x∈P和y∈P∪L,与x 的距离分别为 i－1 和 i 的y 的邻近点的个数都只跟i 有关系,与顶点x 和y 的选取无关.分别利用向量空间,辛空间以及横截设计等构型中2类组合对象间的包含关系定义关联关系构造出距离半正则图,给出图的参数，并给出这些距离半正则图是距离双正则图的条件.

Abstract：

Distance-semiregular graphs are a generalization of distance regular graphs,which have certain regularity and symmetry.A connected bipartite graph with bipartition P∪L is said to be distance-semiregular on P if for each i>0 and any two vertices x∈P and y∈P∪L with distance i,both the number of neighbors of y at distance i－1 from x and the number of neighbors of y at distance i from x do not depend on x or y,but just on i.Several constructions of distance-semiregular graphs are presented in this paper by defining the adjacency relation according to the containment relation between two combinatorial objects from vector space,symplectic space and transversal designs,respectively.This paper gives the parameters of the derived distance-semiregular graphs and the condition for which they are also distance-biregular.

关键词

关键词： 二部图 ; 距离双正则图 ; 向量空间 ; 全迷向子空间 ; 横截设计

Key words： bipartite graph ; distance-biregular graph ; vector space ; totally isotropic subspace ; transversal design

参考文献 15

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