The metric dimension of small distance-regular and strongly regular graphs

نویسنده

  • Robert F. Bailey
چکیده

A resolving set for a graph Γ is a collection of vertices S, chosen so that for each vertex v, the list of distances from v to the members of S uniquely specifies v. The metric dimension of Γ is the smallest size of a resolving set for Γ. A graph is distance-regular if, for any two vertices u, v at each distance i, the number of neighbours of v at each possible distance from u (i.e. i−1, i or i+1) depends only on the distance i, and not on the choice of vertices u, v. The class of distance-regular graphs includes all distance-transitive graphs and all strongly regular graphs. In this paper, we present the results of computer calculations which have found the metric dimension of all distance-regular graphs on up to 34 vertices, low-valency distance transitive graphs on up to 100 vertices, strongly regular graphs on up to 45 vertices, rank-3 strongly regular graphs on under 100 vertices, as well as certain other distance-regular graphs.

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عنوان ژورنال:
  • Australasian J. Combinatorics

دوره 62  شماره 

صفحات  -

تاریخ انتشار 2015