Results 61 to 70 of about 2,530 (150)

Linear combinations of graph eigenvalues

, 2006
Let F(G) be a fixed linear combination of the k extremal eigenvalues of a graph G and of its complement. The problem of finding max{F(G):v(G)=n} generalizes a number of problems raised previously in the literature. We show that the limit max{F(G):v(G)=n}/
Nikiforov, Vladimir
core   +1 more source

On the sum of the two largest Laplacian eigenvalues of trees

, 2014
For S(T), the sum of the two largest Laplacian eigenvalues of a tree T, an upper bound is obtained. Moreover, among all trees with n≥4 vertices, the unique tree which attains the maximal value of S(T) is determined.MSC:05C50.
Mei Guan, M. Zhai, Yongfeng Wu
semanticscholar   +1 more source

Spectral Radius and Hamiltonicity of Graphs

Discussiones Mathematicae Graph Theory, 2019
In this paper, we study the Hamiltonicity of graphs with large minimum degree. Firstly, we present some conditions for a simple graph to be Hamilton-connected and traceable from every vertex in terms of the spectral radius of the graph or its complement,
Yu Guidong, Fang Yi, Fan Yizheng, Cai Gaixiang   +3 more
doaj   +1 more source

Bounds on F-index of tricyclic graphs with fixed pendant vertices

Open Mathematics, 2020
The F-index F(G) of a graph G is obtained by the sum of cubes of the degrees of all the vertices in G. It is defined in the same paper of 1972 where the first and second Zagreb indices are introduced to study the structure-dependency of total π-electron ...
Akram Sana, Javaid Muhammad, Jamal Muhammad   +2 more
doaj   +1 more source

The Maximum Order of Adjacency Matrices With a Given Rank [PDF]

AMS Subject Classification: 05B20, 05C50.Graph;Adjacency ...
Haemers, W.H., Peeters, M.J.P.
core   +1 more source

Graph connectivity and universal rigidity of bar frameworks [PDF]

, 2014
Let $G$ be a graph on $n$ nodes. In this note, we prove that if $G$ is $(r+1)$-vertex connected, $1 \leq r \leq n-2$, then there exists a configuration $p$ in general position in $R^r$ such that the bar framework $(G,p)$ is universally rigid.
Alfakih, A. Y.
core  

Perturbations in a Signed Graph and its Index

Discussiones Mathematicae Graph Theory, 2018
In this paper we consider the behaviour of the largest eigenvalue (also called the index) of signed graphs under small perturbations like adding a vertex, adding an edge or changing the sign of an edge.
Stanić Zoran
doaj   +1 more source

Uniformity in Association schemes and Coherent Configurations: Cometric Q-Antipodal Schemes and Linked Systems [PDF]

2010 Mathematics Subject Classification.
Dam, E.R. van, Martin, W.J., Muzychuk, M.   +2 more
core   +1 more source

A Lower Bound for the Spectral Radius of Graphs with Fixed Diameter [PDF]

AMS classifications: 05C50, 05E99;graphs;spectral radius;diameter;bound;degree ...
Cioaba, S.M., Dam, E.R. van, Koolen, J.H., Lee, J.H.   +3 more
core   +1 more source

Cospectral Graphs and the Generalized Adjacency Matrix [PDF]

AMS classifications: 05C50; 05E99;cospectral graphs;generalized spectrum;generalized adjacency ...
Dam, E.R. van, Haemers, W.H., Koolen, J.H.   +2 more
core   +1 more source