ON THE LAPLACIAN EIGENVALUES OF THE KITE GRAPH

On Laplacian Eigenvalues of a Graph

Let G be a connected graph with n vertices and m edges. The Laplacian eigenvalues are denoted by μ1(G) ≥ μ2(G) ≥ ·· · ≥ μn−1(G) > μn(G) = 0. The Laplacian eigenvalues have important applications in theoretical chemistry. We present upper bounds for μ1(G)+ · · ·+μk(G) and lower bounds for μn−1(G)+ · · ·+μn−k(G) in terms of n and m, where 1 ≤ k ≤ n−2, and characterize the extremal cases. We also ...

Laplacian eigenvalues and optimality: II. The Laplacian of a graph

survey on the rule of the due & hindering relying on the sheikh ansaris ideas

قاعده مقتضی و مانع در متون فقهی کم و بیش مستند احکام قرار گرفته و مورد مناقشه فقهاء و اصولیین می باشد و مشهور معتقند مقتضی و مانع، قاعده نیست بلکه یکی از مسائل ذیل استصحاب است لذا نگارنده بر آن شد تا پیرامون این قاعده پژوهش جامعی انجام دهد. به عقیده ما مقتضی دارای حیثیت مستقلی است و هر گاه می گوییم مقتضی احراز شد یعنی با ماهیت مستقل خودش محرز گشته و قطعا اقتضاء خود را خواهد داشت مانند نکاح که ...

On the Distribution of Laplacian Eigenvalues of a Graph

This paper presents some bounds on the number of Laplacian eigenvalues contained in various subintervals of [0, n] by using the matching number and edge covering number for G, and asserts that for a connected graph the Laplacian eigenvalue 1 appears with certain multiplicity. Furthermore, as an application of our result (Theorem 13), Grone and Merris’ conjecture [The Laplacian spectrum of graph...

On the sum of signless Laplacian eigenvalues of a graph

For a simple graph G, let e(G) denote the number of edges and Sk(G) denote the sum of the k largest eigenvalues of the signless Laplacian matrix of G. We conjecture that for any graph G with n vertices, Sk(G) ≤ e(G) + k+1 2 for k = 1, . . . , n. We prove the conjecture for k = 2 for any graph, and for all k for regular graphs. The conjecture is an analogous to a conjecture by A.E. Brouwer with ...