On Walk Domination: Weakly Toll Domination, l2 and l3 Domination

Pub Date : 2022-11-18 DOI:10.7151/dmgt.2475
M. Gutierrez, S. Tondato
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Abstract

Abstract In this paper we study domination between different types of walks connecting two non-adjacent vertices of a graph. In particular, we center our attention on weakly toll walk and lk-path for k ∈ {2, 3}. A walk between two non-adjacent vertices in a graph G is called a weakly toll walk if the first and the last vertices in the walk are adjacent, respectively, only to the second and second-to-last vertices, which may occur more than once in the walk. And an lk-path is an induced path of length at most k between two non-adjacent vertices in a graph G. We study the domination between weakly toll walks, lk-paths (k ∈ {2, 3}) and different types of walks connecting two non-adjacent vertices u and v of a graph (shortest paths, induced paths, paths, tolled walks, weakly toll walks, lk-paths for k ∈ {3, 4}), and show how these give rise to characterizations of graph classes.
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关于步行统治:弱收费统治,l2和l3统治
摘要本文研究了连接图中两个不相邻顶点的不同类型行走之间的支配关系。特别地,我们将注意力集中在k∈{2,3}的弱收费步行和k-path上。图G中两个不相邻的顶点之间的行走称为弱收费行走,如果行走中的第一个和最后一个顶点分别仅与第二个和倒数第二个顶点相邻,这可能在行走中发生多次。我们研究了弱收费步行(k∈{2,3})和连接图中两个非相邻顶点u和v的不同类型步行(k∈{3,4}的最短路径,诱导路径,路径,收费步行,弱收费步行,k∈{3,4}的k-路径)之间的支配关系,并展示了这些如何产生图类的表征。
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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