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vol. 40 num. 4 lang. pt<![CDATA[SciELO Logo]]>http://www.scielo.cl/img/en/fbpelogp.gif
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<![CDATA[A linear time algorithm for minimum equitable dominating set in trees]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400805&lng=pt&nrm=iso&tlng=pt
Abstract Let G = (V, E) be a graph. A subset D e of V is said to be an equitable dominating set if for every v ∈ V \ D e there exists u ∈ D e such that uv ∈ E and |deg(u) − deg(v)| ≤ 1, where, deg(u) and deg(v) denote the degree of the vertices u and v respectively. An equitable dominating set with minimum cardinality is called the minimum equitable dominating set and its cardinality is called the equitable domination number and it is denoted by γ e . The problem of finding minimum equitable dominating set in general graphs is NP-complete. In this paper, we give a linear time algorithm to determine minimum equitable dominating set of a tree.<![CDATA[Mappings and Decompositions of Pairwise Continuity on <em>(i, j)</em>-almost Lindelöf and <em>(i, j)</em>-weakly Lindelöf Spaces]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400815&lng=pt&nrm=iso&tlng=pt
Abstract The purpose of this paper is to study the effect of mappings and some decompositions of pairwise continuity on (i, j)-almost Lindelöf spaces and (i, j)-weakly Lindelöf spaces. The main results are that an (i, j)-θ-continuous image of an (i, j)-almost Lindelöf space is (i, j)- almost Lindelöf and a pairwise almost continuous image of an (i, j)- weakly Lindelöf space is (i, j)-weakly Lindelöf. We also show that (i, j)-almost Lindelöf, pairwise almost Lindelöf, (i, j)-weakly Lindelöf and pairwise weakly Lindelöf properties are bitopological properties.<![CDATA[Fixed point theorems in fuzzy metric spaces for mappings with B<sub>γ,µ</sub> condition]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400837&lng=pt&nrm=iso&tlng=pt
Abstract In this paper we prove some fixed point theorems in fuzzy metric spaces for a class of generalized nonexpansive mappings satisfying B γ,µ condition. We introduce a type of convexity in fuzzy metric spaces with respect to an altering distance function and prove convergence results for some iteration schemes to the fixed point. The results are supported by suitable examples.<![CDATA[On graded primary-like submodules of graded modules over graded commutative rings]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400859&lng=pt&nrm=iso&tlng=pt
Abstract Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce the concept of graded primary-like submodules as a new generalization of graded primary ideals and give some basic results about graded primary-like submodules of graded modules. Special attention has been paid, when graded submodules satisfies the gr-primeful property, to and extra properties of these graded submodules.<![CDATA[Lyapunov-type inequality for a Riemann-Liouville type fractional boundary value problem with anti-periodic boundary conditions]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400873&lng=pt&nrm=iso&tlng=pt
Abstract In this article, we establish a Lyapunov-type inequality for a two-point Riemann-Liouville type fractional boundary value problem associated with well-posed anti-periodic boundary conditions. As an application, we estimate a lower bound for the eigenvalue of the corresponding fractional eigenvalue problem.<![CDATA[A new approach for Volterra functional integral equations with non-vanishing delays and fractional Bagley-Torvik equation]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400885&lng=pt&nrm=iso&tlng=pt
Abstract A numerical technique for Volterra functional integral equations (VFIEs) with non-vanishing delays and fractional Bagley-Torvik equation is displayed in this work. The technique depends on Bernstein polynomial approximation. Numerical examples are utilized to evaluate the accurate results. The findings for examples figs and tables show that the technique is accurate and simple to use.<![CDATA[Total irregularity strength of some cubic graphs]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400905&lng=pt&nrm=iso&tlng=pt
Abstract Let G = (V;E) be a graph. A total labeling ψ : V ⋃ E → {1, 2, ....k} is called totally irregular total k-labeling of G if every two distinct vertices u and v in V (G) satisfy wt(u) ≠wt(v); and every two distinct edges u 1 u 2 and v 1 v 2 in E(G) satisfy wt(u 1 u 2 ) ≠ wt(v 1 v 2 ); where wt(u) = ψ (u) + ∑ uv∊E(G) ψ(uv) and wt(u 1 u 2 ) = ψ(u 1 ) + ψ(u 1 u 2 ) + ψ(u 2 ): The minimum k for which a graph G has a totally irregular total k-labeling is called the total irregularity strength of G, denoted by ts(G): In this paper, we determine the exact value of the total irregularity strength of cubic graphs.<![CDATA[Line graph of unit graphs associated with finite commutative rings]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400919&lng=pt&nrm=iso&tlng=pt
Abstract For a given graph G, its line graph denoted by L(G) is a graph whose vertex set V (L(G)) = E(G) and {e1, e2} ∈ E(L(G)) if e1 and e2 are incident to a common vertex in G. Let R be a finite commutative ring with nonzero identity and G(R) denotes the unit graph associated with R. In this manuscript, we have studied the line graph L(G(R)) of unit graph G(R) associated with R. In the course of the investigation, several basic properties, viz., diameter, girth, clique, and chromatic number of L(G(R)) have been determined. Further, we have derived sufficient conditions for L(G(R)) to be Planar and Hamiltonian.<![CDATA[Square root stress-sum index for graphs]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400927&lng=pt&nrm=iso&tlng=pt
Abstract The stress of a vertex is a centrality index, which has been introduced by Shimbel (1953). The stress of a vertex in a graph is the number of geodesics (shortest paths) passing through it. In this paper, we introduce a new topological index for graphs called square root stress-sum index using stresses of vertices. Further, we establish some inequalities, obtain some results and compute square root stress-sum index for some standard graphs.<![CDATA[Basarab loop and the generators of its total multiplication group]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400939&lng=pt&nrm=iso&tlng=pt
Abstract A loop (Q, ·) is called a Basarab loop if the identities: (x·yxρ)(xz) = x· yz and (yx)·(xλz ·x) = yz ·x hold. It was shown that the left, right and middle nuclei of the Basarab loop coincide, and the nucleus of a Basarab loop is the set of elements x whose middle inner mapping Tx are automorphisms. The generators of the inner mapping group of a Basarab loop were refined in terms of one of the generators of the total inner mapping group of a Basarab loop. Necessary and sufficient condition(s) in terms of the inner mapping group (associators) for a loop to be a Basarab loop were established. It was discovered that in a Basarab loop: the mapping x ↦ Tx is an endomorphism if and only if the left (right) inner mapping is a left (right) regular mapping. It was established that a Basarab loop is a left and right automorphic loop and that the left and right inner mappings belong to its middle inner mapping group. A Basarab loop was shown to be an automorphic loop (A-loop) if and only if it is a middle automorphic loop (middle Aloop). Some interesting relations involving the generators of the total multiplication group and total inner mapping group of a Basarab loop were derived, and based on these, the generators of the total inner mapping group of a Basarab loop were finetuned. A Basarab loop was shown to be a totally automorphic loop (TA-loop) if and only if it is a commutative and flexible loop. These aforementioned results were used to give a partial answer to a 2013 question and an ostensible solution to a 2015 problem in the case of Basarab loop.<![CDATA[Graphs of edge-to-vertex detour number 2]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400963&lng=pt&nrm=iso&tlng=pt
Abstract For two vertices u and v in a graph G = (V,E), the detour distance D(u, v) is the length of a longest u − v path in G. A u − v path of length D(u, v) is called a u−v detour. For subsets A and B of V, the detour distance D(A, B) is defined as D(A, B) = min{D(x, y) : x ∈ A, y ∈ B}. A u − v path of length D(A, B) is called an A-B detour joining the sets A, B ⊆ V where u ∈ A and v ∈ B. A vertex x is said to lie on an A − B detour if x is a vertex of some A − B detour. A set S ⊆ E is called an edge-to-vertex detour set if every vertex of G is incident with an edge of S or lies on a detour joining a pair of edges of S. The edge-to-vertex detour number dn 2 (G) of G is the minimum order of its edge-to-vertex detour sets and any edge-to-vertex detour set of order dn 2 (G) is an edge-to-vertex detour basis of G. Graphs G of size q for which dn 2 (G)=2 are characterized.<![CDATA[λ-quasi Cauchy sequence of fuzzy numbers]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400981&lng=pt&nrm=iso&tlng=pt
Abstract In this paper we introduce the λ-quasi Cauchy sequence of fuzzy numbers. We obtain the relation between strongly λ-quasi Cauchy convergence and statistically λ-quasi Cauchy convergence for fuzzy numbers.<![CDATA[Equitably strong non-split equitable domination in graphs]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000400989&lng=pt&nrm=iso&tlng=pt
Abstract In a simple, finite and undirected graph G with vertex set V and edge set E, Prof. Sampathkumar defined degree equitability among vertices of G. Two vertices u and v are said to be degree equitable if |deg(u) − deg(v)| ≤ 1. Equitable domination has been defined and studied in [7]. V.R. Kulli and B. Janakiram defined strong non - split domination in a graph [5]. In this paper, the equitable version of this new type of domination is studied.<![CDATA[The probability of an automorphism of an abelian group fixing a group element]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000401001&lng=pt&nrm=iso&tlng=pt
Abstract In this paper, we consider the probability of an automorphism of a finite abelian group fixing a group element. Explicit computations are made to find the fusion classes of finite abelian groups. The probability of an automorphism fixing a group element is obtained in terms of fusion classes. We also compute the bounds of the probability for some particular cases.<![CDATA[On a two-fold cover 2.(2<sup>6</sup>·<em>G</em> <sub><em>2</em></sub> (2)) of a maximal subgroup of Rudvalis group <em>Ru</em>]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000401011&lng=pt&nrm=iso&tlng=pt
Abstract The Schur multiplier M(Ḡ 1) ≅ 4 of the maximal subgroup Ḡ 1 = 26· G 2(2) of the Rudvalis sporadic simple group Ru is a cyclic group of order 4. Hence a full representative group R of the type R = 4.(26· G2(2)) exists for Ḡ 1. Furthermore, Ḡ 1 will have four sets IrrP roj(Ḡ 1, αi) of irreducible projective characters, where the associated factor sets α1, α2, α3 and α4, have orders of 1, 2, 4 and 4, respectively. In this paper, we will deal with a 2-fold cover 2. Ḡ 1 of Ḡ 1 which can be treated as a non-split extension of the form Ḡ = 27· G2(2). The ordinary character table of Ḡ will be computed using the technique of the so-called Fischer matrices. Routines written in the computer algebra system GAP will be presented to compute the conjugacy classes and Fischer matrices of Ḡ and as well as the sizes of the sets |IrrProj(Hi, αi)| associated with each inertia factor Hi. From the ordinary irreducible characters Irr(Ḡ) of Ḡ, the set IrrProj(Ḡ 1, α2) of irreducible projective characters of Ḡ 1 with factor set α2 such that α2 2 = 1, can be obtained.<![CDATA[Lyapunov-type inequality for higher order left and right fractional p-Laplacian problems]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000401031&lng=pt&nrm=iso&tlng=pt
Abstract In this paper, we consider a p-Laplacian eigenvalue boundary value problem involving both right Caputo and left Riemann-Liouville types fractional derivatives. To prove the existence of solutions, we apply the Schaefer’s fixed point theorem. Furthermore, we present the Lyapunov inequality for the corresponding problem.<![CDATA[Fiedler vector analysis for particular cases of connected graphs]]>
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000401041&lng=pt&nrm=iso&tlng=pt
Abstract In this paper, we consider a p-Laplacian eigenvalue boundary value problem involving both right Caputo and left Riemann-Liouville types fractional derivatives. To prove the existence of solutions, we apply the Schaefer’s fixed point theorem. Furthermore, we present the Lyapunov inequality for the corresponding problem.