计算某些外平面图点积维度的高效算法

IF 0.6 4区计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS

International Journal of Foundations of Computer Science Pub Date : 2024-07-12 DOI:10.1142/s0129054124500151

Mahin Bahrami, Dariush Kiani, Zahed Rahmati

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引用次数: 0

摘要

如果存在一个函数[公式：见正文]，使得对于任意两个不同的顶点[公式：见正文]和[公式：见正文]，[公式：见正文]当且仅当[公式：见正文]时，[公式：见正文]称为[公式：见正文]-点积图。公式：见文本]是[公式：见文本]-点积图的最小值[公式：见文本]称为[公式：见文本]的点积维度[公式：见文本]。本文给出了一种计算最多有两个边相交循环的外平面图的点积维度的高效算法。如果图有两个循环，我们只考虑两个循环都有一个共同顶点且其中一个循环的长度大于或等于 6 的外平面图。

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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An Efficient Algorithm to Compute Dot Product Dimension of Some Outerplanar Graphs

A graph [Formula: see text] is called a [Formula: see text]-dot product graph if there is a function [Formula: see text] such that for any two distinct vertices [Formula: see text] and [Formula: see text], [Formula: see text] if and only if [Formula: see text]. The minimum value [Formula: see text] such that [Formula: see text] is a [Formula: see text]-dot product graph, is called the dot product dimension [Formula: see text] of [Formula: see text]. In this paper, we give an efficient algorithm for computing the dot product dimension of outerplanar graphs of at most two edge-disjoint cycles. If the graph has two cycles, we only consider those outerplanar graphs if both cycles have exactly one vertex in common and the length of one of the cycles is greater than or equal to six.

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来源期刊

International Journal of Foundations of Computer Science 工程技术-计算机：理论方法

CiteScore

1.60

自引率

12.50%

发文量

审稿时长

3 months

期刊介绍： The International Journal of Foundations of Computer Science is a bimonthly journal that publishes articles which contribute new theoretical results in all areas of the foundations of computer science. The theoretical and mathematical aspects covered include: - Algebraic theory of computing and formal systems - Algorithm and system implementation issues - Approximation, probabilistic, and randomized algorithms - Automata and formal languages - Automated deduction - Combinatorics and graph theory - Complexity theory - Computational biology and bioinformatics - Cryptography - Database theory - Data structures - Design and analysis of algorithms - DNA computing - Foundations of computer security - Foundations of high-performance computing