Bounds on Roman domination numbers of graphs
Bounds On The Disjunctive Total Domination Number Of A Tree
Let G be a graph with no isolated vertex. In this paper, we study a parameter that is a relaxation of arguably the most important domination parameter, namely the total domination number, γt(G). A set S of vertices in G is a disjunctive total dominating set of G if every vertex is adjacent to a vertex of S or has at least two vertices in S at distance 2 from it. The disjunctive total domination number, [...] γtd(G) , is the minimum cardinality of such a set. We observe that [...] γtd(G)≤γt(G)...
Bounds on the distinguishing chromatic number.
Bounds on the global offensive k-alliance number in graphs
Let G = (V(G),E(G)) be a graph, and let k ≥ 1 be an integer. A set S ⊆ V(G) is called a global offensive k-alliance if |N(v)∩S| ≥ |N(v)-S|+k for every v ∈ V(G)-S, where N(v) is the neighborhood of v. The global offensive k-alliance number is the minimum cardinality of a global offensive k-alliance in G. We present different bounds on in terms of order, maximum degree, independence number, chromatic number and minimum degree.
Bounds on the number of integer valued monotone functions of k integer arguments
Bounds on the Signed 2-Independence Number in Graphs
Let G be a finite and simple graph with vertex set V (G), and let f V (G) → {−1, 1} be a two-valued function. If ∑x∈N|v| f(x) ≤ 1 for each v ∈ V (G), where N[v] is the closed neighborhood of v, then f is a signed 2-independence function on G. The weight of a signed 2-independence function f is w(f) =∑v∈V (G) f(v). The maximum of weights w(f), taken over all signed 2-independence functions f on G, is the signed 2-independence number α2s(G) of G. In this work, we mainly present upper bounds on α2s(G),...
Bounds on the subdominant eigenvalue involving group inverses with applications to graphs
Let be an symmetric, irreducible, and nonnegative matrix whose eigenvalues are . In this paper we derive several lower and upper bounds, in particular on and , but also, indirectly, on . The bounds are in terms of the diagonal entries of the group generalized inverse, , of the singular and irreducible M-matrix . Our starting point is a spectral resolution for . We consider the case of equality in some of these inequalities and we apply our results to the algebraic connectivity of undirected...
Bounds on the Turán density of PG(3, 2).
Branching extent and spectra of trees.
Branching random walks on binary search trees: convergence of the occupation measure
We consider branching random walks with binary search trees as underlying trees. We show that the occupation measure of the branching random walk, up to some scaling factors, converges weakly to a deterministic measure. The limit depends on the stable law whose domain of attraction contains the law of the increments. The existence of such stable law is our fundamental hypothesis. As a consequence, using a one-to-one correspondence between binary trees and plane trees, we give a description of the...
Branching rules for modular representations of symmetric groups, II.
Breaking symmetry on complete bipartite graphs of odd size.
Brève communication. Sur le nombre chromatique des graphes
Brève communication. Transformation du problème de partitionnement en un problème d'ensemble stable de poids maximal
Brève communication. Une caractérisation des graphes chromatiques minimaux sans sommet isolé
Brève communication. Une nouvelle méthode de marquage dans la recherche d'une chaîne de longueur maximale d'un arbre
Bridge and cycle degrees of vertices of graphs.
Bridges and Hamiltonian circuits in planar graphs.
Broken Circuits in Matroids-Dohmen’s Inductive Proof
Dohmen [4] gives a simple inductive proof of Whitney’s famous broken circuits theorem. We generalise his inductive proof to the case of matroids
Broken-cycle-free subgraphs and the log-concavity conjecture for chromatic polynomials.