Distance formula and shortest paths for the (n,k)-star graphs

Authors:
Eddie Cheng;Jerrold W. Grossman;László Lipták;Ke Qiu;Zhizhang Shen
Affiliations:
Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA;Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA;Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA;Department of Computer Science, Brock University, St. Catherines, Ont., Canada L2S 3A1;Department of Computer Science and Technology, Plymouth State University, Plymouth, NH 03264, USA
Venue:
Information Sciences: an International Journal
Year:
2010

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Abstract

The class of (n,k)-star graphs is a generalization of the class of star graphs. Thus a distance formula for the first class implies one for the second. In this paper, we show that the converse is also true. Another important concept is the number of shortest paths between two vertices. This problem has been solved for the star graphs. We will solve the corresponding problem for the (n,k)-star graphs.