Star complements in regular graphs: old and new results

DOI10.1016/j.laa.2009.04.022zbMath1217.05156OpenAlexW2061018285MaRDI QIDQ962113

B. Tayfeh-Rezaie, Peter Rowlinson

Publication date: 6 April 2010

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2009.04.022

zbMATH Keywords

eigenvaluestrongly regular graphstar complement

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (22)

Maximal graphs with a prescribed complete bipartite graph as a star complement ⋮ On joins of a clique and a co-clique as star complements in regular graphs ⋮ On the characterization of graphs by star complements ⋮ Regular and maximal graphs with prescribed tripartite graph as a star complement ⋮ Strong star complements in graphs ⋮ On the multiplicities of digraph eigenvalues ⋮ Eigenvalue multiplicity in triangle-free graphs ⋮ Star complements and connectivity in finite graphs ⋮ Unnamed Item ⋮ Line star sets for Laplacian eigenvalues ⋮ Unions of a clique and a co-clique as star complements for non-main graph eigenvalues ⋮ Star complementary strongly regular decompositions of strongly regular graphs ⋮ Regular star complements in strongly regular graphs ⋮ Graphs with least eigenvalue \(-2\): ten years on ⋮ On bipartite graphs with complete bipartite star complements ⋮ On induced matchings as star complements in regular graphs ⋮ Regular graphs with a prescribed complete multipartite graph as a star complement ⋮ There is no (75,32,10,16) strongly regular graph ⋮ An extension of the star complement technique for regular graphs ⋮ On graphs with prescribed star complements ⋮ On trees as star complements in regular graphs ⋮ Eigenvalue multiplicity in regular graphs

Cites Work

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• Structure and uniqueness of the \((81,20,1,6)\) strongly regular graph
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• Chromatic number and the 2-rank of a graph
• Star complements and switching in graphs
• Harmonic trees
• Star partitions and regularity in graphs
• Interlacing eigenvalues and graphs
• Some characterizations of graphs by star complements
• A simple group of order 44,352,000
• On Moore Graphs with Diameters 2 and 3
• Some properties of the Hoffman-Singleton graph
• Dominating Sets and Eigenvalues of Graphs
• ON THE MULTIPLICITIES OF GRAPH EIGENVALUES
• There are exactly five biplanes with k = 11
• Graphs with least eigenvalue \(-2\): The star complement technique
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