On the metric subgraphs of a graph

IF 0.6 3区 数学 Q3 MATHEMATICS
Yanan Hu, Xingzhi Zhan
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引用次数: 0

Abstract

The three subgraphs of a connected graph induced by the center, annulus and periphery are called its metric subgraphs. The main results are as follows. (1) There exists a graph of order n whose metric subgraphs are all paths if and only if n ≥ 13 and the smallest size of such a graph of order 13 is 22; (2) there exists a graph of order n whose metric subgraphs are all cycles if and only if n ≥ 15, and there are exactly three such graphs of order 15; (3) for every integer k ≥ 3, we determine the possible orders for the existence of a graph whose metric subgraphs are all connected k-regular graphs; (4) there exists a graph of order n whose metric subgraphs are connected and pairwise isomorphic if and only if n ≥ 24 and n is divisible by 3. An unsolved problem is posed.
在图的度量子图上
连通图的中心、环和外围引出的三个子图称为连通图的度量子图。主要结果如下:(1)存在一个n阶图,其度量子图均为路径当且仅当n≥13,且该13阶图的最小尺寸为22;(2)存在一个n阶图,当且仅当n≥15,其度量子图都是圈,且有3个这样的15阶图;(3)对于每一个整数k≥3,我们确定了一个度量子图都是连通k正则图的图存在的可能阶数;(4)存在一个n阶图,当且仅当n≥24且n可被3整除时,其度量子图连通且成对同构。一个未解决的问题被提出。
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来源期刊
Ars Mathematica Contemporanea
Ars Mathematica Contemporanea MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
1.70
自引率
0.00%
发文量
45
审稿时长
>12 weeks
期刊介绍: Ars mathematica contemporanea will publish high-quality articles in contemporary mathematics that arise from the discrete and concrete mathematics paradigm. It will favor themes that combine at least two different fields of mathematics. In particular, we welcome papers intersecting discrete mathematics with other branches of mathematics, such as algebra, geometry, topology, theoretical computer science, and combinatorics. The name of the journal was chosen carefully. Symmetry is certainly a theme that is quite welcome to the journal, as it is through symmetry that mathematics comes closest to art.
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