Results 41 to 50 of about 2,306 (105)

Closed and asymptotic formulas for energy of some circulant graphs

, 2016
We consider circulant graphs G(r,N) where the vertices are the integers modulo N and the neighbours of 0 are {-r,...,-1,1,...,r}. The energy of G(r,N) is a trigonometric sum of N*r terms. For low values of r we compute this sum explicitly.
Arango, Carlos Alberto Marín, Blázquez-Sanz, David   +1 more
core   +1 more source

Eccentricity energy change of complete multipartite graphs due to edge deletion

Special Matrices, 2022
The eccentricity matrix ɛ(G) of a graph G is obtained from the distance matrix of G by retaining the largest distances in each row and each column, and leaving zeros in the remaining ones. The eccentricity energy of G is sum of the absolute values of the
Mahato Iswar, Kannan M. Rajesh
doaj   +1 more source

Graphs whose Laplacian eigenvalues are almost all 1 or 2

Special Matrices
We explicitly determine all connected graphs whose Laplacian matrices have at most four eigenvalues different from 1 and 2.
Mohammadian Ali, Xu Shanshan
doaj   +1 more source

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

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

Some results involving the Aα-eigenvalues for graphs and line graphs

Special Matrices
Let GG be a simple graph with adjacency matrix A(G)A\left(G), degree diagonal matrix D(G),D\left(G), and let l(G)l\left(G) be the line graph of GG. In 2017, Nikiforov defined the Aα{A}_{\alpha }-matrix of GG, Aα(G){A}_{\alpha }\left(G), as a linear ...
da Silva Júnior João Domingos G., Oliveira Carla Silva, da Costa Liliana Manuela G. C.   +2 more
doaj   +1 more source

Eigenvalues and Perfect Matchings [PDF]

AMS classification: 05C50, 05C70, 05E30.graph;perfect matching;Laplacian matrix;eigenvalues.
Brouwer, A.E., Haemers, W.H.
core   +1 more source

Signed graphs with strong (anti-)reciprocal eigenvalue property

Special Matrices
A (signed) graph is said to exhibit the strong reciprocal (anti-reciprocal) eigenvalue property (SR) (resp., (-SR)) if for any eigenvalue λ\lambda , it has 1λ\frac{1}{\lambda } (resp.,−1λ-\frac{1}{\lambda }) as an eigenvalue as well, with the same ...
Belardo Francesco, Huntington Callum
doaj   +1 more source

On Almost Distance-Regular Graphs [PDF]

2010 Mathematics Subject Classification: 05E30, 05C50;distance-regular graph;walk-regular graph;eigenvalues;predistance ...
Dalfo, C., Dam, E.R. van, Fiol, M.A., Garriga, E., Gorissen, B.L.   +4 more
core   +1 more source

On the Laplacian index of tadpole graphs

Special Matrices
In this article, we study the Laplacian index of tadpole graphs, which are unicyclic graphs formed by adding an edge between a cycle Ck{C}_{k} and a path Pn{P}_{n}.
Braga Rodrigo O., Veloso Bruno S.
doaj   +1 more source