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Edge-clique graphs

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Abstract

The edge-clique graphK(G) of a graphG is that graph whose vertices correspond to the edges ofG and where two vertices ofK(G) are adjacent whenever the corresponding edges ofG belong to a common clique. It is shown that every edge-clique graph is a clique graph, and that ifG is either an interval graph or a line graph, then so too isK(G). An algorithm is provided for determining whether a graph is an edge-clique graph. A new graph called the STP graph is introduced and a relationship involving this graph, the edge-clique graph, and the line graph is presented. The STP graphs are also characterized.

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Authors and Affiliations

  1. Western Michigan University, 49008, Kalamanzoo, MI, USA

    Gary Chartrand, S. F. Kapoor & Farrokh Saba

  2. Wright State University, 45435, Dayton, OH, USA

    Terry A. McKee

Authors
  1. Gary Chartrand
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  2. S. F. Kapoor
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  3. Terry A. McKee
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  4. Farrokh Saba
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Additional information

Research supported in part by Office of Naval Research Contract N00014-88-K-0018.

Research supported in part by Office of Naval Research Contract N00014-88-K-0163.

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Chartrand, G., Kapoor, S.F., McKee, T.A. et al. Edge-clique graphs. Graphs and Combinatorics 7, 253–264 (1991). https://doi.org/10.1007/BF01787631

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  • DOI: https://doi.org/10.1007/BF01787631

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