32 citations · 65 across the 15 of their papers we have counts for
20 papers
The quarter-point theorem for Gromov hyperbolic graphs
Walter Carballosa, Jesus Mendez, Rosalio Reyes +1
Gromov hyperbolicity measures the geometric complexity of metric spaces and metric graphs through geodesic triangles and four-point conditions. While calculating the exact continuo…
On the boundary polynomial of a graph
Walter Carballosa, Marcos Masip, Francisco A. Reyes
In this work, we introduce the boundary polynomial of a graph as the ordinary generating function in two variables $B(G;x,y):= \displaystyle\sum_{S\subseteq V(G)} x^{|B(S)|}y^{…
Encoding and Enumerating Acyclic Orientations of Graphs
Walter Carballosa, Jessica Khera, Francisco Reyes
In this work we study the acyclic orientations of graphs. We obtain an encoding of the acyclic orientations of the complete -partite graph with size of its parts $n_1,n_2,\ldots…
Mathematical results on harmonic polynomials
Walter Carballosa, Juan E. Nápoles, J. M Rodríguez +2
Some years ago, the harmonic polynomial was introduced in order to understand better the harmonic topological index; for instance, it allows to obtain bounds of the harmonic index…
Analytical and computational study of the variable inverse sum deg index
Walter Carballosa, J. A. Mendez-Bermudez, Jose M. Rodriguez +1
A large number of graph invariants of the form are studied in mathematical chemistry, where denotes the edge of the graph connecting the ve…
Relations between some topological indices and the line graph
Walter Carballosa, Ana Granados, Domingo Pestana +2
The concepts of geometric-arithmetic and harmonic indices were introduced in the area of chemical graph theory recently. They have proven to correlate well with physical and chemic…
Distinguishing wheel graphs by the alliance polynomial
Walter Carballosa, Omar Rosario, José M. Sigarreta +1
Distinctive power of the alliance polynomial has been studied in previous works, for instance, it has been proved that the empty, path, cycle, complete, complete without one edge a…
Total -domination in Cartesian product of complete graphs
Walter Carballosa, Justin Wisby
Let be a finite undirected graph. A set of vertices in is said to be total -dominating if every vertex in is adjacent to at least vertices in . The…
Hyperbolicity of direct products of graphs
Walter Carballosa, Amauris de la Cruz, Alvaro Martínez-Pérez +1
If is a geodesic metric space and , a {\it geodesic triangle} is the union of the three geodesics , and in…
Independence and matching numbers of some token graphs
Hernan de Alba, Walter Carballosa, Jesús Leaños +1
Let be a graph of order and let . The -token graph of , is the graph whose vertices are the -subsets of , where two vertices a…
Cohen-Macaulayness of triangular graphs
Hernan de Alba, Walter Carballosa, Daniel Duarte +1
We study the Cohen-Macaulay property of triangular graphs . We show that , and are Cohen-Macaulay graphs, and that , , and are not Cohen…
Regularity and Planarity of Token Graphs
Walter Carballosa, Ruy Fabila-Monroy, Jesús Leaños +1
Let be a graph of order and let be an integer. The -token graph of is the graph whose vertices are all the -subsets of , two of which are ad…
Computing the strong alliance polynomial of a graph
Walter Carballosa, Juan Carlos Hernandez-Gomez, Omar Rosario +1
We introduce the strong alliance polynomial of a graph. The strong alliance polynomial of a graph with order n and strong defensive alliance number is the polynomial $a(…
Alliance polynomial of regular graphs
Walter Carballosa, José M. Rodríguez, José M. Sigarreta +1
The alliance polynomial of a graph with order and maximum degree is the polynomial , where is the number of exac…
Gromov hyperbolicity of minor graphs
Walter Carballosa, José M. Rodríguez, Omar Rosario +1
If is a geodesic metric space and , a geodesic triangle is the union of the three geodesics , and in .…
Gromov hyperbolicity in lexicographic product graphs
Walter Carballosa, Amauris de la Cruz, José M. Rodríguez
If is a geodesic metric space and , a {\it geodesic triangle} is the union of the three geodesics , and in…
Solving a conjecture about tessellation graphs of
Walter Carballosa
In the paper Planarity and Hyperbolicity in Graphs, the authors present the following conjecture: every tessellation of the Euclidean plane with convex tiles induces a non-hyperbol…
New inequalities on the hyperbolicity constant of line graphs
Walter Carballosa, José M. Rodríguez, José M. Sigarreta
If X is a geodesic metric space and , a {\it geodesic triangle} is the union of the three geodesics , and in $…
Computing the alliance polynomial of a graph
Walter Carballosa, José M. Rodríguez, José M. Sigarreta +1
The alliance polynomial of a graph with order and maximum degree is the polynomial , where is the number…
Hyperbolicity in the corona and join of graphs
Walter Carballosa, José M. Rodríguez, José M. Sigarreta
If X is a geodesic metric space and , a {\it geodesic triangle} is the union of the three geodesics , and in $…