Results 41 to 50 of about 219 (111)

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

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

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 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

What is a proper graph Laplacian? An operator-theoretic framework for graph diffusion

Special Matrices
We introduce an operator-theoretic definition of a proper graph Laplacian as any matrix associated with a given graph that can be expressed as the composition of a divergence and a gradient operator, with the gradient acting between graph-related spaces ...
Estrada Ernesto
doaj   +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

Signless Laplacian characterization of cones over disjoint unions of cycles, edges and isolated vertices

Special Matrices
Two graphs are said to be Q-cospectral if they share the same signless Laplacian spectrum. A simple graph is said to be determined by its signless Laplacian spectrum (abbreviated as DQS) if there exists no other non-isomorphic simple graph with the same ...
Ye Jiachang, Qian Jianguo, Stanić Zoran
doaj   +1 more source

Spectra of R-Vertex Join and R-Edge Join of Two Graphs

Discussiones Mathematicae - General Algebra and Applications, 2018
The R-graph R(G) of a graph G is the graph obtained from G by intro- ducing a new vertex ue for each e ∈ E(G) and making ue adjacent to both the end vertices of e. In this paper, we determine the adjacency, Lapla- cian and signless Laplacian spectra of R-
Das Arpita, Panigrahi Pratima
doaj   +1 more source

Some stable and closed-shell structures of anticancer drugs by graph theoretical parameters. [PDF]

Heliyon, 2023
Koam ANA, Ahmad A, Azeem M, Hakami KH, Elahi K.   +4 more
europepmc   +1 more source

Sombor spectra of chain graphs. [PDF]

Heliyon, 2023
Imran M, Rather BA.
europepmc   +1 more source