Citation Cvetkovic D, Rowlinson P & Simic S (1999) Some characterizations of graphs by star complements. Linear Algebra and Its Applications, 301 (1-3), pp. 81-97. https://doi.org/10.1016/S0024-3795%2899%2900179-2
Abstract Let μ be an eigenvalue of the graph G with multiplicity k. A star complement for μ in G is an induced subgraph H=G-X such that |X|=k and μ is not an eigenvalue of G-X. Various graphs related to (generalized) line graphs or their complements are characterized by star complements corresponding to eigenvalues -2 or 1.
Keywords graph; eigenvalue; star complement
Journal Linear Algebra and Its Applications: Volume 301, Issue 1-3