| Summary: | 碩士 === 國立暨南國際大學 === 資訊工程學系 === 97 === Let e be an edge in a graph G. The labeling of e, denoted by r(e), is a positive integer. An edge ranking of graph G is a labeling of edges such that every path between two different edges ei, ej with r(ei) = r(ej) contains an intermediate edge ew with r(ew) > r(ei). An edge ranking is called a minimum edge ranking of G if its largest rank is minimum among all rankings of G. The edge ranking problem is to find a minimum edge ranking of graph G. The problem has been proved to be an NP-hard problem. It is known that there are polynomial time algorithms for non-trivial classes, such as trees and two-connected outerplanar graphs. Our algorithm is an O(1) time algorithm to find the minimum edge ranking on S(n, 3) graphs where S(n, k) is a Sierpinski graph consisting of all n-tuples of integers 1, 2, . . . , k.
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