On the connected monophonic number of a graph

Abstract

For a connected graph G of order at least two, a connected monophonic set of G is a monophonic set S such that the subgraph induced by S is connected. The minimum cardinality of a connected monophonic set of G is the connected monophonic number of G and is denoted by . The number of extreme vertices and cut-vertices of G is its extreme-cut order . A graph G is an extreme-cut connected monophonic graph if . Some interesting results on the extreme-cut connected monophonic graphs G are studied. For positive integers r, d and with r

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图的连通单音数

对于至少为二阶的连通图G, G的连通单音集是单音集S，使得S引出的子图是连通的。G的连通单音集的最小基数是G的连通单音数，表示为。G的极值顶点和切割顶点的个数就是它的极值切割阶数。图G是一个极切连通单音图。研究了关于极切连通单音图G的一些有趣的结果。对于正整数r、d和r

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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