科研之友
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摘要
Given a graph G with m >= 1 edges, the non-backtracking spectral radius of G is the spectral radius of its non-backtracking matrix B(G) defined as the 2m x 2m matrix where each edge uv is represented by two rows and two columns, one per orientation: (u, v) and (v, u), and the entry of B(G) in row (u,v) and column (x, y) is given by delta(vx)(1 - delta(uy)), with delta(ij) being the Kronecker delta. A tight upper bound is given for the non-backtracking spectral radius in terms of the spectral radius of the adjacency matrix and minimum degree, and those connected graphs that maximize the non-backtracking spectral radius are determined if the connectivity (edge connectivity, bipartiteness, respectively) is given.
