The minimum orientable genus of the repeated Cartesian product of graphs

IF 0.9 4区 数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Marietta Galea, John Baptist Gauci
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引用次数: 0

Abstract

Determining the minimum genus of a graph is a fundamental optimisation problem in the study of network design and implementation as it gives a measure of non-planarity of graphs. In this paper, we are concerned with determining the smallest value of g such that a given graph G has an embedding on the orientable surface of genus g. In particular, we consider the Cartesian product of graphs since this is a well studied graph operation which is often used for modeling interconnection networks. The s-cube \(Q_i^{(s)}\) is obtained by taking the repeated Cartesian product of i complete bipartite graphs \(K_{s,s}\). We determine the genus of the Cartesian product of the 2r-cube with the repeated Cartesian product of cycles and of the Cartesian product of the 2r-cube with the repeated Cartesian product of paths.

图的重复笛卡尔积的最小可定向格
图的最小格值的确定是网络设计和实现研究中的一个基本优化问题,因为它给出了图的非平面性的度量。在本文中,我们关注的是确定g的最小值,使得给定的图g在g属的可定向表面上有一个嵌入。特别是,我们考虑图的笛卡尔积,因为这是一个研究得很好的图操作,经常用于互连网络的建模。s立方\(Q_i^{(s)}\)是通过取i个完全二部图的重复笛卡尔积\(K_{s,s}\)得到的。我们确定了2r-立方体的笛卡尔积与循环的重复笛卡尔积的属,以及2r-立方体的笛卡尔积与路径的重复笛卡尔积的属。
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来源期刊
Journal of Combinatorial Optimization
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
83
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.
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