7 papers
Null Decomposition of Unicyclic Graphs
Luiz Emilio Allem, Daniel Alejandro Jaume, Gonzalo Molina +2
In this work we obtain basis for the null space of unicyclic graphs. We extend the null decomposition of trees from [11] for unicyclic graphs. As an application, we obtain closed f…
Independence and Matching Numbers of Unicyclic Graphs From Null Space
Luiz Emilio Allem, Daniel Alejandro Jaume, Gonzalo Molina +2
We characterize unicyclic graphs that are singular using the support of the null space of their pendant trees. From this, we obtain closed formulas for the independence and matchin…
Short note on Randić energy
Luiz Emilio Allem, Gonzalo Molina, Adrián Pastine
In this paper, we consider the Randić energy of simple connected graphs. We provide upper bounds for in terms of the number of vertices and the nullity of the graph. We p…
On the null structure of bipartite graphs without cycles of length a multiple of 4
Daniel A. Jaume, Gonzalo Molina, Adrián Pastine
In this work we study the null space of bipartite graphs without cycles of length multiple of , and its relation to structural properties. We decompose them into two subgraphs:…
Maximum and minimum nullity of a tree degree sequence
Gonzalo Molina, Daniel A. Jaume
The nullity of a graph is the multiplicity of the eigenvalue zero in its adjacency spectrum. In this paper, we give a closed formula for the minimum and maximum nullity among trees…
A - and sparsest basis for the null space of a forest in optimal time
Daniel A. Jaume, Gonzalo Molina, Adrián Pastine +1
Given a matrix, the Null Space Problem asks for a basis of its null space having the fewest nonzeros. This problem is known to be NP-complete and even hard to approximate. The null…