Journal of Mathematical Chemistry

, Volume 9, Issue 4, pp 297–305 | Cite as

A möbius inversion of the ulam subgraphs conjecture

  • Milan Kunz
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Abstract

The generalized Eichinger matrices are defined asE =Σjn1(δjSTS)−1, whereδj M denotes the matrixM withj th row and column deleted.S is the incidence matrix andMT is the transposed matrix. The conjectureS T SE = S K TS K , where SK is the incidence matrix of the complete graph, is proven for trees, simple cycles and complete graphs. The consequence of the conjecture isS G TS G (E G -I) = S G TS G , whereG is the complementary graph ofG. It leads to graphs with imaginary arcs as the complements of graphs with multiple arcs.

Keywords

Physical Chemistry Complete Graph Incidence Matrix Simple Cycle Complementary Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© J.C. Baltzer AG, Scientific Publishing Company 1992

Authors and Affiliations

  • Milan Kunz
    • 1
  1. 1.ChemopetrolResearch Institute of Macromolecular ChemistryBrnoCzechoslovakia

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