无爪三次图中的半全数强迫

Pub Date : 2023-01-01 DOI:10.7151/dmgt.2501

Yijuan Liang, Jie Chen, Shou-Jun Xu

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引用次数: 0

摘要

对于无隔离图G = (V (G)， E (G))，如果集合S是G的一个强迫集(或零强迫集)，且S中的每个顶点与S的另一个顶点的距离在2以内，则称其为G的半强迫集。半衰期强迫数f2 (G)是G中半衰期强迫集的最小基数。本文证明了如果G (cid:54) = k4是一个n阶的连通无爪三次图，则F t 2 (G)≤38n + 1。在这个界内达到相等的图被表示为图的无限集。

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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Semitotal forcing in claw-free cubic graphs

For an isolate-free graph G = ( V ( G ) , E ( G )), a set S ⊆ V ( G ) is called a semitotal forcing set of G if it is a forcing set (or a zero forcing set) of G and every vertex in S is within distance 2 of another vertex of S . The semitotal forcing number F t 2 ( G ) is the minimum cardinality of a semitotal forcing set in G . In this paper, we prove that if G (cid:54) = K 4 is a connected claw-free cubic graph of order n , then F t 2 ( G ) ≤ 38 n + 1. The graphs achieving equality in this bound are characterized, an inﬁnite set of graphs.

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