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Intervals and Convex Sets in Strong Product of Graphs

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Abstract

In this note we consider intervals and convex sets of strong product. Vertices of an arbitrary interval of \({G\boxtimes H}\) are classified with shortest path properties of one factor and a walk properties of a slightly modified second factor. The convex sets of the strong product are characterized by convexity of projections to both factors and three other local properties, one of them being 2-convexity.

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Authors and Affiliations

  1. Institute of Mathematics and Physics, FEECS, University of Maribor, Smetanova 17, 2000, Maribor, Slovenia

    Iztok Peterin

  2. Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000, Ljubljana, Slovenia

    Iztok Peterin

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  1. Iztok Peterin
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Peterin, I. Intervals and Convex Sets in Strong Product of Graphs. Graphs and Combinatorics 29, 705–714 (2013). https://doi.org/10.1007/s00373-012-1144-4

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  • DOI: https://doi.org/10.1007/s00373-012-1144-4

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