ELA Linear Combinations of Graph Eigenvalues 331
نویسنده
چکیده
Let µ 1 (G) ≥. .. ≥ µn (G) be the eigenvalues of the adjacency matrix of a graph G of order n, and G be the complement of G. Suppose F (G) is a fixed linear combination of µ i (G) , µ n−i+1 (G) , µ i G ¡ , and µ n−i+1 G ¡ , 1 ≤ i ≤ k. It is shown that the limit lim n→∞ 1 n max {F (G) : v (G) = n} always exists. Moreover, the statement remains true if the maximum is taken over some restricted families like " Kr-free " or " r-partite " graphs. It is also shown that 29 + √ 329 42 n − 25 ≤ max v(G)=n µ 1 (G) + µ 2 (G) ≤ 2 √ 3 n. This inequality answers in the negative a question of Gernert.
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تاریخ انتشار 2006