On pitfalls in computing the geodetic number of a graph
نویسندگان
چکیده
Given a simple connected graph G = (V, E) the geodetic closure I[S] ⊂ V of a subset S of V is the union of all sets of nodes lying on some geodesic (or shortest path) joining a pair of nodes vk, vl ∈ S. The geodetic number, denoted by g(G), is the smallest cardinality of a node set S∗ such that I[S∗] = V . In “The geodetic number of a graph”, Mathematical and Computer Modelling 17 (June 1993) 89–95, F. Harary, E. Loukakis and C. Tsouros propose an incorrect algorithm to find the geodetic number of a graph G. We provide counterexamples and show why the proposed approach must fail. We then develop a 0-1 integer programming model to find the geodetic number. Computational results are given.
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ورودعنوان ژورنال:
- Optimization Letters
دوره 1 شماره
صفحات -
تاریخ انتشار 2007