Revistas académicas de la Universidad Católica del Norte
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The edge geodetic fault tolerant domination number of a graph
No full textFor a connected graph G = (V, E), a set F⊆V is said to be an edge geodetic fault tolerant dominating set of G if F is both edge geodetic set and fault tolerant dominating set of G. The minimum cardinality of an edge geodetic fault tolerant dominating set of G is called the edge geodetic fault tolerant domination number of G and is denoted by γgeft(G). The edge geodetic fault tolerant domination number of certain classes of graphs are determined. It is shown that for each pair of integers 3 ≤a < b, there exists a connected graph G such that γ(G) = a, γge (G)= b and γgeft(G) = a + b-1, where γ(G), ge γ(G) and γgeft(G) are the domination number, edge geodetic domination number and edge geodetic fault tolerant domination number of G respectively
Nourishing Number of Some Associated Graphs
No full textLet N0 = N∪{0} and P(N0) be the power set. An injection f : V (G) → P(N0) is an integer additive set-indexer (IASI) of a graph G if the induced map f+ : E(G) → P(N0) given by f+(uv) = f(u) + f(v) is also an injection, where f(u) + f(v) is the sumset of f(u) and f(v). Moreover, if |f+(uv)| = |f(u)| |f(v)|, for all uv in E(G), then f is a strong IASI of G. The nourishing number of a graph G is the minimum order of the maximal complete subgraph of G such that G admits a strong IASI. In this paper we investigate the admissibility of strong IASI for some associated graphs and calculate their nourishing number. In addition, we obtain the nourishing number of powers of the associated graphs
Characterizations of reversible rings relating k-potents
No full textThis article embodies a ring theoretic property that preserves the reversibility at non zero k-potents. The structure of k-potents in k-reversible and pseudo k-reversible rings are studied in connection with various kinds of ring extensions. A ring R is said to be k-reversible if and only if ab ∈ K(R) for a,b ∈ R implies ab = ba; and a ring R is called pseudo k-reversible if 0 ̸= ab ∈ K(R) for a,b ∈ K(R) implies ab = ba, where K(R) is the set of all k-potents in R. It is proved that k-reversible rings are pseudo k-reversible but the converse is not true in general. Under certain conditions the polynomial rings of pseudo k-reversible inherit the character of pseudo k-reversible rings
Stability and boundedness criteria for certain second-order nonlinear neutral stochastic functional differential equations
No full textThis paper presents stochastic stability and stochastic boundedness to certain second-order nonlinear neutral stochastic differential equations. The second-order differential equation is weakened to a neutral stochastic system of first-order equations and used together with a second-order quadratic function to obtain perfect Lyapunov-Krasovskii functional. This functional is adapted and applied to obtain criteria on the nonlinear functions to ensure novel results on stochastic stability and stochastic asymptotic stability of the zero solution. Furthermore, when the forcing term is nonzero, fresh results on stochastic boundedness and uniform stochastic boundedness of solutions are obtained. The results of this paper are original, new, essentially improving, complementing, and simplifying several related ones in the literature. Two special cases of the theoretical results are supplied to demonstrate the applicability of the hypothetical results
Notes on multiplicative generalized (σ, τ )-reverse derivations with Lie ideals of semiprime ∗-rings
No full textThis article is devoted to investigation into the notion of multiplicative generalized(σ,τ)-reverse derivations associated with(σ,τ)-reverse derivations of semiprime∗-rings is characterized. The action of these derivations on∗-Lie ideals of semiprime∗-rings is also consideration. Moreover, the commutativity of semiprime∗-rings ad-mitting multiplicative generalized(σ,τ)-reverse derivations associated with(σ,τ)-reverse derivations satisfying certain algebraic identitieson∗-Lie ideals is explored
On the spectrum and main eigenvalues of k-half graphs
No full textA chain graph is a bipartite graph in which the neighborhood of the vertices in each partite set formsa chain with respect to set inclusion. By extending the concept of nesting from a bipartite graph to a k-partitegraph, a k-nested graph is defined. The half graph is a chain graph having no pairs of duplicatevertices. Similarly, the ’k-half graph’ is a class of k-nested graph without any duplicate vertices. Westudy some spectral properties of a k-half graph. We prove that a k-half graph on kn vertices has exactlyn main eigenvalues and there are 2k downer vertices with respect to each eigenvalue of its adjacencymatrix. We show the existence of 3(kC2) edges in a k-half graph on kn vertices, which are 2-downer for afew eigenvalues
The Connected and Forcing Connected Restrained Monophonic Numbers of a Graph
No full textFor a connected graph G = (V,E) of order at least two, a connected restrained monophonic set S of G is a restrained monophonic set such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected restrained monophonic set of G is the connected restrained monophonic number of G and is denoted by mcr(G). We determine bounds for it and find the same for some special classes of graphs. It is shown that, if a, b and p are positive integers such that 3 ≤ a ≤ b ≤ p, p−1 6= a, p−1 6= b, then there exists a connected graph G of order p, mr(G) = a and mcr(G) = b. Also, another parameter forcing connected restrained monophonic number fcrm(G) of a graph G is introduced and several interesting results and realization theorems are proved
Some bounds onfirst degcity index
No full textThe first degcity index DC1(G) of a connected graph G is defined as the sum of the terms [ex+ey][dx+dy] over all the lines xy of G, where dx and ex represents the degree and eccentricity of a point x in G respectively. In this article, we have obtained some lower and upper bounds of first degcity index
Antimagic Labeling for Some Snake Graphs
No full textA graph with q edges is called antimagic if its edges can be labeled with 1, 2, 3, ..., q without repetition such that the sums of the labels of the edges incident to each vertex are distinct. In this paper we study antimagic labeling of double triangular snake, alternate triangular snake, double alternate triangular snake, quadrilateral snake, double quadrilateral snake, alternate quadrilateral snake, double alternate quadrilateral snake
A variant of Banach’s contraction principle in ordered Banach spaces
No full textIn this article we establish a version of Banach’s contraction principle in ordered Banach spaces. This version is adapted to prove existence and uniqueness results for an integral equation or a boundary value problem depending on the derivative