Finding the edge ranking number through vertex partitions

Authors:
Yo-Lin Lin;Justie Su-Tzu Juan;Yue-Li Wang
Affiliations:
Department of Computer Science and Information Engineering, National Chi Nan University, Puli, Nantou 54561, Taiwan;Department of Computer Science and Information Engineering, National Chi Nan University, Puli, Nantou 54561, Taiwan;Department of Information Management, National Taiwan University of Science and Technology, Taipei 10607, Taiwan
Venue:
Discrete Applied Mathematics
Year:
2013

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Abstract

An edge coloring c^':E-{1,2,...,t} of a graph G=(V,E) is an edge t-ranking if for any two edges of the same color, every path between them contains an intermediate edge with a larger color. The edge ranking number @g"r^'(G) is the smallest value of t such that G has an edge t-ranking. In this paper, we introduce a relation between edge ranking number and vertex partitions. By using the proposed recurrence formula, we show that the edge ranking number of the Sierpinski graph @g"r^'(S(n,k))=n@g"r^'(K"k) for any n,k=2 where K"k denotes a complete graph of k vertices.