arXiv subjects
Publications and source records attributed to Pedro Díaz Navarro.
By finding orthogonal representation for a family of simple connected called $δ$-graphs it is possible to show that $δ$-graphs satisfy delta conjecture. An extension of the argument to graphs of the form $\overline{P_{Δ(G)+2}\sqcup G}$ where $P_{Δ(G)+2}$ is a path and $G$ is a simple connected graph it is possible to find an orthogonal representation of $\overline{P_{Δ(G)+2}\sqcup G}$ in $\mathbb{R}^{Δ(G)+1}$. As a consequence we prove delta conjecture.
In this paper we give a technique to represent simple connected graphs by using Clockwise Circular Representations and we show its applications by calculating orthogonal representations of simple connected graphs which are essentials in matrix analysis and graph theory.
In this paper we proof that any cactus graph satisfies graph complement conjecture by finding a orthogonal representation of its complement in $\mathbb{R}^5$.
In this paper we define two infinite families of graphs called C-$δ$ graphs and $δ$- graph and prove that $δ$-graphs satisfy $δ$ conjecture. Also we introduce a family of C-$δ$ graphs from which we can identify $δ$ graphs as their complements. Finally we give a list of C-$δ$ graphs and the relationship with their minimum semidefinite rank.