Fe b 20 03 On the largest eigenvalue of a random subgraph of the hypercube ∗
نویسندگان
چکیده
Let G be a random subgraph of the n-cube where each edge appears randomly and independently with probability p. We prove that the largest eigenvalue of the adjacency matrix of G is almost surely λ1(G) = (1 + o(1))max ( ∆(G), np ) , where ∆(G) is the maximum degree of G and the o(1) term tends to zero as max(∆(G), np) tends to infinity.
منابع مشابه
Se p 20 02 On the largest eigenvalue of a random subgraph of the hypercube ∗
Let G be a random subgraph of the n-cube where each edge appears randomly and independently with small probability p. We prove that the largest eigenvalue of the adjacency matrix of G is almost surely λ1(G) = (1 + o(1))max ( ∆(G), np ) , where ∆(G) is the maximum degree of G and the o(1) term tends to zero as max(∆(G), np) tends to infinity.
متن کاملOn the Largest Eigenvalue of a Random Subgraph of the Hypercube
Let G be a random subgraph of the n-cube where each edge appears randomly and independently with probability p. We prove that the largest eigenvalue of the adjacency matrix of G is almost surely λ1(G) = (1 + o(1))max ( 1/2(G), np ) , where (G) is the maximum degree ofG and theo(1) term tends to zero as max( 1/2(G), np) tends to infinity.
متن کاملThe spectrum of the hyper-star graphs and their line graphs
Let n 1 be an integer. The hypercube Qn is the graph whose vertex set isf0;1gn, where two n-tuples are adjacent if they differ in precisely one coordinate. This graph has many applications in Computer sciences and other area of sciences. Inthe graph Qn, the layer Lk is the set of vertices with exactly k 1’s, namely, vertices ofweight k, 1 k n. The hyper-star graph B(n;k) is...
متن کاملCounting the number of spanning trees of graphs
A spanning tree of graph G is a spanning subgraph of G that is a tree. In this paper, we focus our attention on (n,m) graphs, where m = n, n + 1, n + 2, n+3 and n + 4. We also determine some coefficients of the Laplacian characteristic polynomial of fullerene graphs.
متن کاملJu l 2 00 1 On the largest eigenvalue of a sparse random subgraph
We consider a sparse random subraph of the n-cube where each edge appears independently with small probability p(n) = O(n−1+o(1)). In the most interesting regime when p(n) is not exponentially small we prove that the largest eigenvalue is ∆(G)1/2(1+o(1)) = n log 2 log(p−1) × (1+o(1)) almost surely,where ∆(G) is the maximum degree of G. If p(n) is exponentially small but not proportional to 2−n/...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003