无连接总支配细分的 Np 完备性和边界

IF 0.9 4区数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Combinatorial Optimization Pub Date : 2024-12-14 DOI:10.1007/s10878-024-01245-4

Canan Çiftçi, Aysun Aytaç

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引用次数: 0

摘要

一个子集\( S\subseteq V(G) \)，其中V(G)是图G的顶点集，如果每个顶点在S中有一个邻居或在S中至少有两个距离为2的顶点，则是G的析取总支配集。这种集合的最小基数是析取的总支配数。在图的边或顶点上有一些图的修改，其中之一是对边进行细分。G的析取总控制细分数是为了增加析取总控制数而必须细分的最小边数（G中的每条边只能细分一次）。首先证明了二部图的析取全控制细分问题是np完全的。然后，我们建立了析取全控制细分的一些界。

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Np-completeness and bounds for disjunctive total domination subdivision

A subset \( S\subseteq V(G) \), where V(G) is the vertex set of a graph G, is a disjunctive total dominating set of G if each vertex has a neighbour in S or has at least two vertices in S at distance two from it. The minimum cardinality of such a set is the disjunctive total domination number. There are some graph modifications on the edge or vertex of a graph, one of which is subdividing an edge. The disjunctive total domination subdivision number of G is the minimum number of edges which must be subdivided (each edge in G can be subdivided exactly once) to increase the disjunctive total domination number. Firstly, we prove that the disjunctive total domination subdivision problem is NP-complete in bipartite graphs. We next establish some bounds on disjunctive total domination subdivision.

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来源期刊

Journal of Combinatorial Optimization 数学-计算机：跨学科应用

CiteScore

2.00

自引率

10.00%

发文量

审稿时长

6 months

期刊介绍： The objective of Journal of Combinatorial Optimization is to advance and promote the theory and applications of combinatorial optimization, which is an area of research at the intersection of applied mathematics, computer science, and operations research and which overlaps with many other areas such as computation complexity, computational biology, VLSI design, communication networks, and management science. It includes complexity analysis and algorithm design for combinatorial optimization problems, numerical experiments and problem discovery with applications in science and engineering. The Journal of Combinatorial Optimization publishes refereed papers dealing with all theoretical, computational and applied aspects of combinatorial optimization. It also publishes reviews of appropriate books and special issues of journals.