【摘 要】
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Let C(n, △; c) be the class of c-cyclic graphs with maximum degree △ and n vertices.In this talk, we characterize all the extremal graphs that achieve the sma
【机 构】
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TongjiUniversity,Shanghai200092,China
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Let C(n, △; c) be the class of c-cyclic graphs with maximum degree △ and n vertices.In this talk, we characterize all the extremal graphs that achieve the smallest Laplacian spectral radius of C(n, △; c) for 0 ≤ c ≤ (△-1)(△-2).We also characterize the unique extremal graph that achieves the largest Laplacian spectral radius of C(n, △; 1)when △≥ [-n+2/3] and d4 ≥ 2 or △ ≥ [n/3] +1 and d4 =1, respectively.We also prove that for two unicyclic graphs G and G on n vertices, if △(G) ≥ [11n/30]+2 and △(G) ＞ △(G),then λ(G) ＞ λ(G), and the bound "[11n/30] +2" is best possible.
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