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Centers of chordal graphs

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Abstract

In a graphG = (V, E), theeccentricity e(S) of a subset S\( \subseteq \) ismax x ∈ V min y ∈ S d(x, y); ande(x) stands fore({x}). Thediameter ofG ismax x ∈ V e(x), theradius r(G) ofG ismin x ∈ V e(x) and theclique radius cr(G) ismin e(K) whereK runs over all cliques. Thecenter ofG is the subgraph induced byC(G), the set of all verticesx withe(x) = r(G). Aclique center is a cliqueK withe(K) = cr(G). In this paper, we study the problem of determining the centers of chordal graphs. It is shown that the center of a connected chordal graph is distance invariant, biconnected and of diameter no more than 5. We also prove that2cr(G) ≤ d(G) ≤ 2cr(G) + 1 for any connected chordal graphG. This result implies a characterization of a biconnected chordal graph of diameter 2 and radius 1 to be the center of some chordal graph.

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Authors and Affiliations

  1. Department of Applied Mathematics, National Chiao Tung University, 30050, Hsinchu, Taiwan, Republic of China

    Gerard J. Chang

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  1. Gerard J. Chang
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Supported by the National Science Council of the Republic of China under grant NSC77-0208-M008-05

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Chang, G.J. Centers of chordal graphs. Graphs and Combinatorics 7, 305–313 (1991). https://doi.org/10.1007/BF01787637

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  • DOI: https://doi.org/10.1007/BF01787637

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