# Walter Carballosa

• Electr. J. Comb.
• 2013
If X is a geodesic metric space and x1, x2, x3 ∈ X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. If X is hyperbolic, we denote(More)
A nonempty set S ⊂ V is a defensive k-alliance in G = (V,E), k ∈ [−Δ,Δ] ∪ Z, if for every v ∈ S, dS(v) ≥ dS̄(v) + k. A defensive k-alliance S is called exact, if S is defensive k-alliance but is no defensive (k+1)-alliance in G. In this paper we study the mathematical properties of exact defensive k-alliances in graphs. In particular, we obtain several(More)
• Electr. J. Comb.
• 2011
If X is a geodesic metric space and x1, x2, x3 ∈ X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. We denote by δ(X) the sharp(More)
• Electronic Notes in Discrete Mathematics
• 2014
The main aim in this work is to obtain quantitative information about the distortion of the hyperbolicity constant of the graph G \ e (respectively, G/e ) obtained from the graph G by deleting (respectively, contracting) an arbitrary edge e from it. A graph H is a minor of a graph G if a graph isomorphic to H can be obtained from G by contracting some(More)
• Electr. J. Comb.
• 2012
If X is a geodesic metric space and x1, x2, x3 ∈ X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δneighborhood of the union of the other two sides, for every geodesic triangle T in X. We denote by δ(X) the sharp(More)
• Discrete Applied Mathematics
• 2017
The alliance polynomial of a graphGwith order n andmaximumdegree∆ is the polynomial A(G; x) = ∆ k=−∆ Ak(G) x n+k, where Ak(G) is the number of exact defensive k-alliances in G. We obtain some properties of A(G; x) and its coefficients for regular graphs. In particular, we characterize the degree of regular graphs by the number of non-zero coefficients of(More)
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