The Laplacian spectral radius of graphs on surfaces
نویسندگان
چکیده
منابع مشابه
The Spectral Radius of Graphs on Surfaces
This paper provides new upper bounds on the spectral radius ρ (largest eigenvalue of the adjacency matrix) of graphs embeddable on a given compact surface. Our method is to bound the maximum rowsum in a polynomial of the adjacency matrix, using simple consequences of Euler’s formula. Let γ denote the Euler genus (the number of crosscaps plus twice the number of handles) of a fixed surface Σ. Th...
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Let C(n, k) be the set of all unicyclic graphs with n vertices and cycle length k. For anyU ∈ C(n, k),U consists of the (unique) cycle (say Ck) of length k and a certain number of trees attached to the vertices of Ck having (in total) n − k edges. If there are at most two trees attached to the vertices of Ck, where k is even, we identify in the class of unicyclic graphs those graphs whose Lapla...
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Given a connected graph G, the Randić index R(G) is the sum of 1 √ d(u)d(v) over all edges {u, v} of G, where d(u) and d(v) are the degree of vertices u and v respectively. Let q(G) be the largest eigenvalue of the singless Laplacian matrix of G and n = |V (G)|. Hansen and Lucas (2010) made the following conjecture:
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2008
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.08.032