C. Oliveira

activity

20132023

most citedThe clique number and the smallest Q-eigenvalue of graphs

1 citations · 1 across the 7 of their papers we have counts for

collaborators

9 papers

cs.DM2023

Bounds for a alpha-eigenvalues

João Domingos G. da Silva, Carla Silva Oliveira, Liliana Manuela G. C. da Costa

Let G be a graph with adjacency matrix A(G) and degree diagonal matrix D(G). In 2017, Nikiforov [1] defined the matrix Aalpha(G), as a convex combination of A(G) and D(G), the foll…

cs.DM2022

Spectral Heuristics Applied to Vertex Reliability

Carla Silva Oliveira, Fausto Marques Pinheiro Junior, Jose Andre de Moura Brito

The operability of a network concerns its ability to remain operational, despite possible failures in its links or equipment. One may model the network through a graph to evaluate…

cs.DM2022

On the characteristic polynomial of the $A_{α}$ -matrix for some operations of graphs

João Domingos G. da Silva, Carla Silva Oliveira, Liliana Manuela G. C. da Costa

Let G be a graph of order $n$ with adjacency matrix $A (G)$ and diagonal matrix of degree $D (G)$ . For every $α \in [0, 1]$ , Nikiforov \cite{VN17} defined the matrix $A_α(G) = αD(G) +…

math.CO2020

Laplacian integral graphs with a given degree sequence constraint

Anderson Fernandes Novanta, Carla S. Oliveira, Leonardo S. de Lima

Let G be a graph on n vertices. The Laplacian matrix of G, denoted by L(G), is defined as L(G) = D(G) - A(G), where A(G) is the adjacency matrix of G and D(G) is the diagonal matri…

math.GM2020

On the Graovac-Ghorbani index for bicyclic graphs with no pendant vertices

Diego Pacheco, Leonardo de Lima, Carla Silva Oliveira

Let $G = (V, E)$ be a simple undirected and connected graph on $n$ vertices. The Graovac--Ghorbani index of a graph $G$ is defined as $$ABC_{GG}(G)= \sum_{uv \in E(G)} \sqrt{\frac{n_{…

math.CO2015★ 1 cited

The clique number and the smallest Q-eigenvalue of graphs

Leonardo de Lima, Vladimir Nikiforov, Carla Oliveira

Let $q_{m i n} (G)$ stand for the smallest eigenvalue of the signless Laplacian of a graph $G$ of order $n .$ This paper gives some results on the following extremal problem: How larg…

math.SP2014

A lower bound for the sum of the two largest signless Laplacian eigenvalues

Leonardo de Lima, Carla Oliveira

Let $G$ be a graph of order $n \geq 3$ with sequence degree given as $d_{1} (G) \geq ... \geq d_{n} (G)$ and let $μ_{1} (G), ..., μ_{n} (G)$ and $q_{1} (G), ..., q_{n} (G)$ be the Laplacian and…

math.SP2014

Spectra of the blow-up graphs

Carla Oliveira, Leonardo de Lima, Vladimir Nikiforov

Let $G$ be graph on $n$ vertices and $G^{(t)}$ its blow-up graph of order $t .$ In this paper, we determine all eigenvalues of the Laplacian and the signless Laplacian matrix of $G^…

math.SP2013

Extremal graphs for the sum of the two largest signless Laplacian eigenvalues

Carla Silva Oliveira, Leonardo de Lima, Paula Rama +1

Let G be a simple graph on $n$ vertices and $e (G)$ edges. Consider $Q (G) = D + A$ as the signless Laplacian of $G$ , where $A$ is the adjacency matrix and $D$ is the diagonal matrix…