GRAPH

Graph theoretical results obtained by the support of the expert system “Graph” -- an extended survey. GRAPH is an interactive package, developed as an expert system in the 80s at the University of Belgrade, aimed to support research in graph theory by helping to pose, verify or disprove conjectures. The present article surveys 92 papers, mostly in spectral graph theory, which results were obtained with the support of GRAPH. The results presented are divided into the following sections: Tables of graphs. The largest eigenvalue of a graph. The second largest eigenvalue of a graph. Graphs with least eigenvalue bounded by $-2$. Integral graphs. Graph angles. Star complements. Graphs sharing specified properties with their complements. Miscellaneous results. Combinatorial optimization.


References in zbMATH (referenced in 22 articles )

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  1. Eichner, Martin (ed.); Halloran, M. Elizabeth (ed.); O’Neill, Philip D. (ed.): Design and analysis of infectious disease studies. Abstracts from the workshop held February 18--24, 2018 (2018)
  2. Furtula, Boris; Gutman, Ivan: Borderenergetic graphs of order 12 (2017)
  3. Larson, C. E.; van Cleemput, N.: Automated conjecturing. III. Property-relations conjectures (2017)
  4. Larson, C. E.; Van Cleemput, N.: Automated conjecturing. I: Fajtlowicz’s Dalmatian heuristic revisited (2016)
  5. Aouchiche, Mustapha; Caporossi, Gilles; Hansen, Pierre: Open problems on graph eigenvalues studied with AutoGraphiX (2013)
  6. Aouchiche, M.; Hansen, P.: A survey of automated conjectures in spectral graph theory (2010)
  7. Aouchiche, M.; Bell, F. K.; Cvetković, D.; Hansen, P.; Rowlinson, P.; Simić, S. K.; Stevanović, D.: Variable neighborhood search for extremal graphs. 16. Some conjectures related to the largest eigenvalue of a graph (2008)
  8. Christophe, Julie; Dewez, Sophie; Doignon, Jean-Paul; Fasbender, Gilles; Grégoire, Philippe; Huygens, David; Labbé, Martine; Elloumi, Sourour; Mélot, Hadrien; Yaman, Hande: Linear inequalities among graph invariants: using GraPHedron to uncover optimal relationships (2008)
  9. Mélot, Hadrien: Facet defining inequalities among graph invariants: The system graphedron (2008)
  10. de Abreu, Nair Maria Maia: Old and new results on algebraic connectivity of graphs (2007)
  11. Stevanović, Dragan; de Abreu, Nair M. M.; de Freitas, Maria A. A.; Del-Vecchio, Renata: Walks and regular integral graphs (2007)
  12. Brankov, V.; Hansen, P.; Stevanović, D.: Automated conjectures on upper bounds for the largest Laplacian eigenvalue of graphs (2006)
  13. Aouchiche, Mustapha; Hansen, Pierre: Variable neighborhood search for extremal graphs. XIII: Girth (2005)
  14. Cvetković, Dragoš; Simić, Slobodan: Graph theoretical results obtained by the support of the expert system “Graph” -- an extended survey (2005)
  15. Fajtlowicz, Siemion (ed.); Fowler, Patrick W. (ed.); Hansen, Pierre (ed.); Janowitz, Melvin F. (ed.); Roberts, Fred S. (ed.): Graphs and discovery. Proceedings of the DIMACS working group, computer-generated conjectures from graph theoretic and chemical databases, November 12--16, 2001, and DIMACS public event, graph theory day 42, November 10, 2001, Piscataway, NJ, USA. (2005)
  16. Bell, Francis K.; Simić, Slobodan K.: On graphs whose star complement for (-2) is a path or a cycle (2004)
  17. Caporossi, Gilles; Hansen, Pierre: Variable neighborhood search for extremal graphs. V: Three ways to automate finding conjectures (2004)
  18. Hansen, Pierre; Mélot, Hadrien: Computers and discovery in algebraic graph theory (2002)
  19. Simić, Slobodan; Gutman, Ivan; Baltić, Vladimir: Some graphs with extremal Szeged index (2000)
  20. Cvetković, Dragoš; Simić, Slobodan: On graphs whose second largest eigenvalue does not exceed ((\sqrt5-1)/2) (1995)

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