图的总边斯坦纳数

IF 0.5 Q3 MATHEMATICS

Annals of the University of Craiova-Mathematics and Computer Science Series Pub Date : 2021-06-30 DOI:10.52846/ami.v48i1.1361

J. John

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引用次数: 0

摘要

G的总边Steiner集是W的边Steiner集，使得由诱导出的子图没有孤立顶点。G的总边斯坦纳集的最小基数是G的总边斯坦纳数，用ste(G)表示。研究了该概念所满足的一些一般性质。研究了一类图的总边斯坦纳数。对总边为2或3的p阶连通图进行了刻画。给出了总边斯坦纳数为p或p−1的必要条件。证明了对于2≤a < b和b > a+ 1的整数对a和b，存在一个使se(G) = a和ste(G) = b的连通图G，并且证明了对于4≤a < b和b > a+ 1的整数对a和b，存在一个使st(G) = a和ste(G) = b的连通图G。

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The total edge Steiner number of a graph

A total edge Steiner set of G is an edge Steiner set W such that the subgraph induced by has no isolated vertex. The minimum cardinality of a total edge Steiner set of G is the total edge Steiner number of G and is denoted by ste(G). Some general properties satisfied by this concept are studied. The total edge Steiner numbers of certain classes of graphs is studied. Connected graphs of order p with total edge Steiner number 2 or 3 are characterized. Necessary conditions for total edge Steiner number to be p or p − 1 is given. It is shown that for every pair a and b of integers with 2 ≤ a a+ 1, there exists a connected graph G such that se(G) = a and ste(G) = b. Also it shown that for every pair a and b of integers with 4 ≤ a a + 1, there exists a connected graph G such that st(G) = a and ste(G) = b.

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来源期刊

Annals of the University of Craiova-Mathematics and Computer Science Series MATHEMATICS-

CiteScore

1.10

自引率

10.00%

发文量