On unicyclic graphs whose second largest eigenvalue dose not exceed 1

Abstract We discuss the question of classifying the connected simple graphs H for which the second largest eigenvalue of the signless Laplacian Q(H) is ≤ 4. We discover that the question is inextricable linked to a knapsack problem with infinitely many allowed weights. We take the first few steps towards the general solution. We prove that this class of graphs is minor closed.

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On the estimation of the second largest eigenvalue of Markov ciphers

Security and Communication Networks ◽

10.1002/sec.1465 ◽

2016 ◽

pp. n/a-n/a

Author(s):

Weijia Xue ◽

Tingting Lin ◽

Xin Shun ◽

Fenglei Xue ◽

Xuejia Lai

Keyword(s):

Largest Eigenvalue ◽

Second Largest Eigenvalue

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On the second largest eigenvalue of the generalized distance matrix of graphs

Linear Algebra and its Applications ◽

10.1016/j.laa.2020.05.028 ◽

2020 ◽

Vol 603 ◽

pp. 226-241

Author(s):

Abdollah Alhevaz ◽

Maryam Baghipur ◽

Hilal Ahmad Ganie

Keyword(s):

Distance Matrix ◽

Largest Eigenvalue ◽

Second Largest Eigenvalue ◽

Generalized Distance

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The second largest eigenvalue upper bound for the canonical genetic algorithms

International Journal of Knowledge-based and Intelligent Engineering Systems ◽

10.3233/kes-2007-11305 ◽

2007 ◽

Vol 11 (3) ◽

pp. 193-198

Author(s):

Parag C. Pendharkar

Keyword(s):

Genetic Algorithms ◽

Upper Bound ◽

Largest Eigenvalue ◽

Second Largest Eigenvalue

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Distance spectral radius of unicyclic graphs with fixed maximum degree

Journal of Algebra and Its Applications ◽

10.1142/s0219498820500681 ◽

2019 ◽

Vol 19 (04) ◽

pp. 2050068

Author(s):

Hezan Huang ◽

Bo Zhou

Keyword(s):

Spectral Radius ◽

Connected Graph ◽

Maximum Degree ◽

Distance Matrix ◽

The Other ◽

Connected Graphs ◽

Largest Eigenvalue ◽

Unicyclic Graphs ◽

The Largest Eigenvalue

The distance spectral radius of a connected graph is the largest eigenvalue of its distance matrix. For integers [Formula: see text] and [Formula: see text] with [Formula: see text], we prove that among the connected graphs on [Formula: see text] vertices of given maximum degree [Formula: see text] with at least one cycle, the graph [Formula: see text] uniquely maximizes the distance spectral radius, where [Formula: see text] is the graph obtained from the disjoint star on [Formula: see text] vertices and path on [Formula: see text] vertices by adding two edges, one connecting the star center with a path end, and the other being a chord of the star.

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