The gonality of queen's graphs

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-07-30 DOI:10.1016/j.disc.2024.114186

引用次数: 0

Abstract

In this paper we study queen's graphs, which encode the moves by a queen on an $n \times m$ chess board, through the lens of chip-firing games. We prove that their gonality is equal to nm minus the independence number of the graph, and give a one-to-one correspondence between maximum independent sets and classes of positive rank divisors achieving gonality. We also prove an identical result for toroidal queen's graphs.

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王后图形的整体性

在本文中，我们通过芯片发射博弈的视角研究了皇后图，皇后图编码了皇后在 n×m 国际象棋棋盘上的走法。我们证明了它们的整体性等于 nm 减去图的独立数，并给出了最大独立集与实现整体性的正秩除数类之间的一一对应关系。我们还证明了环状皇后图的相同结果。

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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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.