关于1步控制图的一些结果

Mathematica Montisnigri Pub Date : 1900-01-01 DOI:10.20948/MATHMON-2019-44-2

M. F. Jalalvand, N. J. Rad, M. Ghorani

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引用次数: 2

摘要

图G中的一个精确的1步支配集是G的顶点的子集S，使得()1 N v S对于每个顶点()v v G。如果一个图包含一个精确1步控制集，那么它就是一个精确1步控制图。本文给出了精确1步控制图大小的新上界。我们还给出了精确1步控制树的总控制数的上界，并描述了在该上界上达到相等的树。

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Some results on the exact 1-step domination graphs

An exact 1-step dominating set in a graph G is a subset S of vertices of G such that ( ) 1 N v S   for every vertex ( ) v V G  . A graph is an exact 1-step domination graph if it contains an exact 1-step dominating set. In this paper, we obtain new upper bounds on the size of exact 1-step domination graphs. We also present an upper bound on the total domination number of an exact 1-step domination tree and characterize trees achieving equality for this bound.

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Mathematica Montisnigri

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