Computing the Sum of k Largest Laplacian Eigenvalues of Tricyclic Graphs

IF 1 Q1 MATHEMATICS
Pawan Kumar, S. Merajuddin, S. Pirzada
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引用次数: 0

Abstract

Let G ( V, E ) be a simple graph with | V ( G ) | = n and | E ( G ) | = m . If S k ( G ) is the sum of k largest Laplacian eigenvalues of G , then Brouwer’s conjecture states that S k ( G ) ≤ m + k ( k +1)2 for 1 ≤ k ≤ n . The girth of a graph G is the length of a smallest cycle in G . If g is the girth of G , then we show that the mentioned conjecture is true for 1 ≤ k ≤ (cid:98) g − 22 (cid:99) . Wang et al. [ Math. Comput. Model. 56 (2012) 60–68] proved that Brouwer’s conjecture is true for bicyclic and tricyclic graphs whenever 1 ≤ k ≤ n with k (cid:54) = 3 . We settle the conjecture under discussion also for tricyclic graphs having no pendant vertices when k = 3 .
计算三环图的k个最大拉普拉斯特征值和
设G (V, E)是一个简单图,其中| V (G) | = n, |e (G) | = m。如果sk (G)是G的k个最大拉普拉斯特征值的和,则Brouwer猜想表明,当1≤k≤n时,sk (G)≤m + k (k +1)2。图G的周长是图G中最小环的长度。如果g是g的周长,那么我们证明了上述猜想对于1≤k≤(cid:98) g−22 (cid:99)成立。Wang et al.[数学]第一版。Model. 56(2012) 60-68]证明了当1≤k≤n且k (cid:54) = 3时,Brouwer猜想对双环和三环图成立。对于k = 3时无垂点的三环图,我们也解决了讨论中的猜想。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Discrete Mathematics Letters
Discrete Mathematics Letters Mathematics-Discrete Mathematics and Combinatorics
CiteScore
1.50
自引率
12.50%
发文量
47
审稿时长
12 weeks
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