Fat Hoffman graphs with smallest eigenvalue at least $-1-τ$
نویسندگان
چکیده
In this paper, we show that all fat Hoffman graphs with smallest eigenvalue at least −1−τ , where τ is the golden ratio, can be described by a finite set of fat (−1 − τ)-irreducible Hoffman graphs. In the terminology of Woo and Neumaier, we mean that every fat Hoffman graph with smallest eigenvalue at least −1−τ is anH-line graph, where H is the set of isomorphism classes of maximal fat (−1−τ)-irreducible Hoffman graphs. It turns out that there are 37 fat (−1−τ)-irreducible Hoffman graphs, up to isomorphism.
منابع مشابه
Fat Hoffman graphs with smallest eigenvalue greater than -3
In this paper, we give a combinatorial characterization of the special graphs of fat Hoffman graphs containing K1,2 with smallest eigenvalue greater than −3, where K1,2 is the Hoffman graph having one slim vertex and two fat vertices.
متن کاملThe spectrum and toughness of regular graphs
In 1995, Brouwer proved that the toughness of a connected k-regular graph G is at least k/λ − 2, where λ is the maximum absolute value of the non-trivial eigenvalues of G. Brouwer conjectured that one can improve this lower bound to k/λ − 1 and that many graphs (especially graphs attaining equality in the Hoffman ratio bound for the independence number) have toughness equal to k/λ. In this pape...
متن کاملOn distance-regular graphs with smallest eigenvalue at least -m
A non-complete geometric distance-regular graph is the point graph of a partial geometry in which the set of lines is a set of Delsarte cliques. In this paper, we prove that for fixed integer m ≥ 2, there are only finitely many non-geometric distance-regular graphs with smallest eigenvalue at least −m, diameter at least three and intersection number c2 ≥ 2.
متن کاملOn the limit points of the smallest eigenvalues of regular graphs
In this paper, we give infinitely many examples of (non-isomorphic) connected k-regular graphs with smallest eigenvalue in half open interval [−1− √ 2,−2) and also infinitely many examples of (non-isomorphic) connected k-regular graphs with smallest eigenvalue in half open interval [α1,−1− √ 2) where α1 is the smallest root(≈ −2.4812) of the polynomial x3 + 2x2 − 2x − 2. From these results, we ...
متن کاملOn the Second Least Distance Eigenvalue of a Graph
Let G be a connected graph on n vertices, and let D(G) be the distance matrix of G. Let ∂1(G) ≥ ∂2(G) ≥ · · · ≥ ∂n(G) denote the eigenvalues of D(G). In this paper, the connected graphs with ∂n−1(G) at least the smallest root of x3 − 3x2 − 11x− 6 = 0 are determined. Additionally, some non-isomorphic distance cospectral graphs are given.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1111.7284 شماره
صفحات -
تاریخ انتشار 2011