Revistas académicas de la Universidad Católica del Norte
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On the eigenvalues of the distance signless Laplacian matrix of graphs
No full textLet G be a connected graph and let DQ(G) be the distance signless Laplacian matrix of G with eigenvalues ρ1≥ ρ2≥…≥ ρn. The spread of the matrix DQ}(G) is defined as s(DQ(G)) := maxi,j| ρi-ρj| = ρ1- ρn. We derive new bounds for the distance signless Laplacian spectral radius ρ1 of G. We establish a relationship between the distance signless Laplacian energy and the spread of DQ(G). For a real number α ≠ 0, the graph invariant mα (G) is the sum of the α -th power of the distance signless Laplacian eigenvalues of G. Finally, we obtain various bounds for the graph invariant mα(G)
Rainbow Mean Index of Some Classes of Graphs
No full textIn this article, we determine the rainbow mean index of cartesianproductG◻Pn, where G is a regular graph;Pm◻Pn; Wn◻K2;total graph of paths; chain of cycles and complete graphs; triangular treeand join graphs tCs∨K1
Fixed point and stability of nonlinear differential equations with variable delays
No full textIn this paper, we study the stability of a generalized nonlinear differential equation with variable delays via fixed point theory. An asymptotic stability theorem with sufficient conditions is proved, which improves and generalizes some previous results. Two examples are given to illustrate our results
Isostrophy invariant elastic property
No full textThe queried ``if there any finite universal elastic property loop that is not a middle Bol loop" is still open in the theoretical study of loops. The solution of the above open problem is found at the neighbourhood of the study of universal elastic law and its generalization termed elastic law. In this paper, the invariant elastic property under the isostrophy of loops were studied. Necessary and sufficient condition for the invariant elasticity is found. It was shown that commutative loops with invariant elastic property are inverse property loops. In particular, it was revealed that a commutative inverse property loops with universal elastic property are generalized Moufang loops
Homeomorphisms of the real line with singularities
No full textGiven a real number a ≠ 0, we consider the set of homeomorphisms f: R\{0}→ R \{a} where{(x, y):x=0}is a vertical asymtote, {(x, y):y=a} is a horizontal asymtote and f is strictly increasing in each connected component (−∞,0) and (0,+∞). In this context, similar to circle homeomorphisms, all possible dynamics are shown. It is established the relationship between existence of periodic orbits and the limit sets. Also, whenever f−n(0) ≠a for all n ∈ N, then the non-existence of periodic orbits leads to a non-trivial limit set, which is either the whole line R or perfect and nowhere dense. It is shown a notion of separation of points that leads to transitivit
A characterization of σ-prime rings involving generalized derivations
No full textThis paper’s major goal is to work on commutativity of σ-prime rings with second kind involution σ, involving generalized derivation satisfy the certain differential identities. Finally, we provide some examples to demonstrate that the conditions assumed in our results are not unnecessar
An optimization model for fuzzy nonlinear programming with Beale's conditions using trapezoidal membership functions
No full textNon-linear Programming (NLP) is an optimization technique for determining the optimum solution to a broad range of research issues. Many times, the objective function is non-linear, owing to various economic behaviors such as demand, cost, and many others. Since the appearance of Kuhn and Tucker's fundamental theoretical work, a general NLP problem can be resolved using many methods to find the optimum solution. In this chapter, a fuzzy mathematical model based on Beale's condition is proposed to address NLP with inequality constraints in terms of fuzziness. Furthermore, the model demonstrates how quadratic programming problems can be solved using membership functions. The model also describes three stages: that is, mathematical formulation, computational procedures, and numerical illustration with comparative analysis. Likewise, the model illustrates the considered problem using two distinct approaches, namely membership functions (MF) and robust ranking index. Finally, the comparison analysis provides detailed results and discussion that justify the optimal outcome in order to address the vagueness of certain NLPPs
Investigating Banhatti indices on the molecular graph and the line graph of Glass with M-polynomial approach
No full textTopological indices are numerical values related to a chemical structure that describes the correlation of chemical structure with different physical properties and chemical reactions. Glass has wide applications in architecture, tableware, optics, and optoelectronics.
In this article, first, the mathematical relationship between M-polynomial and Banhatti indices such as K-Banhatti, d-Banhatti, and hyper d-Banhatti indices are obtained. Then using M-polynomial, Banhatti indices are calculated
Some inequalities between degree- and distance-based topological indices
No full textThe first Zagreb index M1 and the second Zagreb index M2 belong to the class of degree-based topological indices which are defined for a simple connected graph G with vertex set V = {υ1, υ2, ··· , υn} as M1(G) = Pn ı˙=1 d2 ı˙ and M2(G) = Pυı˙∼υj˙ dı˙dj˙, where dı˙ is the degree of vertex υi and υı˙ ∼ υj˙ represents the adjacency of vertices υı˙ and υj˙ in G. The eccentric connectivity index (ECI) is a distance based topological index, denoted by ξc, is defined as ξc(G) = Pni=1 εı˙dı˙, where εı˙ is the eccentricity of υı˙ in G. The aim of this paper is to derive the inequalities between ECI and the Zagreb indices. Moreover, we establish the inequalities between some variants of ECI and the Zagreb indices
Monophonic-triangular Distance in Graphs
No full textA path u1, u2, ..., un in a connected graph G such that for i, j with j ≥ i + 3, there does not exist an edge uiuj , is called a monophonic-triangular path or mt-path. The monophonic-triangular distance or mt-distance dmt(u, v) from u to v is defined as the length of a longest u−v mt-path in G. The mt-eccentricity emt(v) of a vertex v in G is defined as the maximum mt-distance between v and other vertices in G. The mt-radius radmt(G) is defined as the minimum mt-eccentricity among the vertices of G and the mt-diameter diammt(G) is defined as the maximum mt-eccentricity among the vertices of G. It is shown that radmt(G) ≤ diammt(G) for every connected graph G. Some realization and characterization results are given based on mt-radius, mt-diameter, mt-center and mt-periphery of a connected graph