16 papers
On the Extremal Energy of Complex Unit Gain Dumbbell Graphs
Silin Huang, Kevin Pereyra
We study the extremal energy problem for complex unit gain graphs whose underlying graph is the dumbbell graph . Using switching equivalence, we reduce the spectrum t…
A Ridge-Saturation Characterization of -Critical Graphs
Do Trong Hoang, Vadim E. Levit, Eugen Mandrescu +1
We characterize the graphs which are simultaneously -critical and members of the class . The characterization is stated in three equivalent languages. In the graph…
The 2-Quasi-Regularizability Conjecture and Independence Polynomials of Wp Graphs
Kevin Pereyra
Hoang, Levit, Mandrescu and Pham asked for structural conditions ensuring that the independence polynomial of a $\W_p$ graph is log-concave, or at least unimodal, and conjectured t…
On the Determinant of KÅnig-Egerváry Graphs
Kevin Pereyra
Several graph decompositions that factorize the determinant of the adjacency matrix isolate a KÅnig-Egerváry part, such as the SD--KE decomposition and the critical independence…
On the nullspace of split graphs
Daniel A. Jaume, Victor N. Schvöllner, Cristian Panelo +1
We study the nullspace of the adjacency matrix of split graphs, whose vertex set can be partitioned into a clique and an independent set. We introduce the clique-kernel, a subspace…
Graphs with core(G) = nucleus(G)
Vadim E. Levit, Eugen Mandrescu, Kevin Pereyra
Let be a finite simple graph. An independent set of is critical if for every independent set o…