Pablo Romero

collaborators

6 papers

math.CO2025

Construction of infinitely many trace-minimal graphs with maximum number of spanning trees

Pablo Romero, Louis Petingi

A longstanding problem in spectral graph theory asks for graphs with maximum number of spanning trees among all connected simple graphs with a prescribed number of vertices and edg…

math.CO2025

Existence, uniqueness and construction of locally most reliable two-terminal graphs

Pablo Romero

A two-terminal graph is a graph G equipped with two vertices in V(G) called terminals. Let T(n,m) be the set of two-terminal graphs on n vertices and m edges. Let G be in T(n,m) an…

math.CO2025

Existence of most reliable two-terminal graphs with distance constraints

Pablo Romero

A two-terminal graph is a simple graph equipped with two distinguished vertices, called terminals. Let $T_{n, m}$ be the class consisting of all nonisomorphic two-terminal graphs on…

math.CO2025

Characterization of locally most split reliable graphs

Pablo Romero

A two-terminal graph is a graph equipped with two distinguished vertices, called terminals. Let $T_{n, m}$ be the set of all nonisomorphic connected simple two-terminal graphs on $n…

math.CO2024

An algebraic characterization of strong graphs

Pablo Romero

Let $G$ be a connected simple graph on $n$ vertices and $m$ edges. Denote $N_{i}^{(j)} (G)$ the number of spanning subgraphs of $G$ having precisely $i$ edges and not more than $j$ …

math.CO2024

There are finitely many uniformly most reliable graphs of corank 5

Pablo Romero

If $G$ is a simple graph and $ρ \in [0, 1]$ , the reliability $R_{G} (ρ)$ is the probability of $G$ being connected after each of its edges is removed independently with probability $ρ$ .…