Discussiones Mathematicae Graph Theory 31(4) (2011) 753-761
doi: 10.7151/dmgt.1577

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Spanning Tree Congestion of Rook's Graphs

Kyohei Kozawa

Electric Power Development Co., Ltd.
6--15--1, Ginza, Chuo-ku, Tokyo, 104--8165, Japan

Yota Otachi

Graduate School of Information Sciences
Tohoku University
Sendai 980--8579, Japan

Abstract

Let G be a connected graph and T be a spanning tree of G. For e ∈ E(T), the congestion of e is the number of edges in G joining the two components of T −e. The congestion of T is the maximum congestion over all edges in T. The spanning tree congestion of G is the minimum congestion over all its spanning trees. In this paper, we determine the spanning tree congestion of the rook's graph Km ☐ Kn for any m and n.

Keywords: spanning tree congestion, Rook's graph

2010 Mathematics Subject Classification: 05C05 (05C76).

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Received 3 August 2010
Revised 15 November 2010
Accepted 15 November 2010