H-extension of graphs

Abstract

We consider the problem of constructing a graphG* from a collection of isomorphic copies of a graphG in such a way that for every two copies ofG, either no vertices or a section graph isomorphic to a graphH is identified. It is shown that ifG can be partitioned into vertex-disjoint copies ofH, thenG* can be made to have at most |H| orbits. A condition onG so thatG* can be vertextransitive is also included.

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References

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    C. Berge,Graphs and Hypergraphs, North-Holland Publishing Company, 1973.

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    H. H. Teh andS. C. Shee,Algebraic Theory of Graphs, Lee Kong Chian Institute of Mathematics and Computer Science, Nanyang University, Singapore 1976.

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Shee, S.C., Teh, H.H. H-extension of graphs. Combinatorica 4, 207–211 (1984). https://doi.org/10.1007/BF02579222

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AMS subject classification (1980)

  • 05 C 10
  • 05 C 25