Abstract
The geodetic number of a graph is an important graph invariant. In 2002, Atici showed the geodetic set determination of a graph is an NP-Complete problem. In this paper, we compute the geodetic set and geodetic number of an important class of graphs called the k-th power of a cycle. This class of graphs has various applications in Computer Networks design and Distributed computing. The k-th power of a cycle is the graph that has the same set of vertices as the cycle and two different vertices in the k-th power of this cycle are adjacent if the distance between them is at most k.
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference16 articles.
1. The geodetic number of a graph;Kim;J. Appl. Math. Comput.,2004
2. On the geodetic number of a graph
3. Realizable ratios in graph theory: Geodesic parameters;Chartrand;Bull. Inst. Comb. Appl.,1999
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