Multiplicities of Eigenvalues and Tree-Width of Graphs
نویسنده
چکیده
Definition 1. OG is the set of real symmetric V_V matrices with entries ai, j such that ai, j<0 if [i, j] # E and ai, j=0 if i{ j and [i, j] E. An operator A # OG has a non-degenerate first eigenvalue *1 (groundstate) if G is connected (Perron and Frobenius). The invariant +(G) is defined using multiplicities of the second eigenvalue *2 for some real symmetric matrix A # OG . Moreover, +(G) is related to the genus of G : +(G) 3 if and only if G is planar and more generally +(G) 4 genus(G)+3. Recently, Lova sz and Schrijver [20] proved that linklessly Article No. TB981834
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عنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 74 شماره
صفحات -
تاریخ انتشار 1998