Results 71 to 80 of about 2,691 (126)

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

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

The minimum exponential atom-bond connectivity energy of trees

Special Matrices
Let G=(V(G),E(G))G=\left(V\left(G),E\left(G)) be a graph of order nn. The exponential atom-bond connectivity matrix AeABC(G){A}_{{e}^{{\rm{ABC}}}}\left(G) of GG is an n×nn\times n matrix whose (i,j)\left(i,j)-entry is equal to ed(vi)+d(vj)−2d(vi)d(vj){e}^
Gao Wei
doaj   +1 more source

A sharp lower bound on the signless Laplacian index of graphs with (κ,τ)-regular sets

Special Matrices, 2018
A new lower bound on the largest eigenvalue of the signless Laplacian spectra for graphs with at least one (κ,τ)regular set is introduced and applied to the recognition of non-Hamiltonian graphs or graphs without a perfect matching.
Andeelić Milica, Cardoso Domingos M., Pereira António   +2 more
doaj   +1 more source

Enumeration of Cospectral Graphs [PDF]

AMS classification: 05C50;graphs;eigenvalues ...
Haemers, W.H., Spence, E.
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

A formula for all minors of the adjacency matrix and an application

Special Matrices, 2014
We supply a combinatorial description of any minor of the adjacency matrix of a graph. This descriptionis then used to give a formula for the determinant and inverse of the adjacency matrix, A(G), of agraph G, whenever A(G) is invertible, where G is ...
Bapat R. B., Lal A. K., Pati S.
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

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

Divisible Design Graphs [PDF]

AMS Subject Classification: 05B05, 05E30, 05C50.Strongly regular graph;Group divisible design;Deza graph;(v;k ...
Haemers, W.H., Kharaghani, H., Meulenberg, M.A.   +2 more
core   +1 more source