Graphs with the Reduced Spectrum in the Unit Interval
Aleksandar Torgašev (1984)
Publications de l'Institut Mathématique
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Aleksandar Torgašev (1984)
Publications de l'Institut Mathématique
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Zhibo Chen (2004)
Czechoslovak Mathematical Journal
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The construction of the extended double cover was introduced by N. Alon [1] in 1986. For a simple graph with vertex set , the extended double cover of , denoted , is the bipartite graph with bipartition where and , in which and are adjacent iff or and are adjacent in . In this paper we obtain formulas for the characteristic polynomial and the spectrum of in terms of the corresponding information of . Three formulas are derived for the number of spanning trees...
Tingzeng Wu, Heping Zhang (2017)
Discussiones Mathematicae Graph Theory
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A graph is said to be characterized by its permanental spectrum if there is no other non-isomorphic graph with the same permanental spectrum. In this paper, we investigate when a complete bipartite graph Kp,p with some edges deleted is determined by its permanental spectrum. We first prove that a graph obtained from Kp,p by deleting all edges of a star K1,l, provided l < p, is determined by its permanental spectrum. Furthermore, we show that all graphs with a perfect matching obtained...
Mieczyslaw Borowiecki (1985)
Publications de l'Institut Mathématique
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Aleksandar Torgašev (1982)
Publications de l'Institut Mathématique
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Jill Faudree, Ralph J. Faudree, Ronald J. Gould, Michael S. Jacobson, Brent J. Thomas (2017)
Discussiones Mathematicae Graph Theory
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A graph G is H-saturated if H is not a subgraph of G but the addition of any edge from G̅ to G results in a copy of H. The minimum size of an H-saturated graph on n vertices is denoted sat(n,H), while the maximum size is the well studied extremal number, ex(n,H). The saturation spectrum for a graph H is the set of sizes of H saturated graphs between sat(n,H) and ex(n,H). In this paper we completely determine the saturation spectrum of stars and we show the saturation spectrum of paths...
Jan Dereziński (1998-1999)
Séminaire Équations aux dérivées partielles
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A method to study the embedded point spectrum of self-adjoint operators is described. The method combines the Mourre theory and the Limiting Absorption Principle with the Feshbach Projection Method. A more complete description of this method is contained in a joint paper with V. Jakić, where it is applied to a study of embedded point spectrum of Pauli-Fierz Hamiltonians.
W. Marek, K. Rasmussen
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CONTENTS0. Motivation, results to be used in the sequel ................51. Slicing ’s ..........................................................102. Hereditarily countable, definable elements ................133. Spectrum of L.............................................................154. The width of elements of spectrum ............................195. Non-uniform strong definability ..................................266. Solution to a problem of Wilmers................................327....