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Similar Journals
 Opuscula MathematicaJournal Prestige (SJR): 0.378 Citation Impact (citeScore): 1Number of Followers: 108     Open Access journal ISSN (Print) 1232-9274 - ISSN (Online) 2300-6919 Published by AGH University of Science and Technology Press  [8 journals]
• Upper bounds for the extended energy of graphs and some extended
equienergetic graphs

• Authors: Chandrashekar Adiga, B. R. Rakshith
Pages: 5 - 13
Abstract: In this paper, we give two upper bounds for the extended energy of a graph one in terms of ordinary energy, maximum degree and minimum degree of a graph, and another bound in terms of forgotten index, inverse degree sum, order of a graph and minimum degree of a graph which improves an upper bound of Das et al. from [On spectral radius and energy of extended adjacency matrix of graphs, Appl. Math. Comput. 296 (2017), 116-123]. We present a pair of extended equienergetic graphs on $$n$$ vertices for $$n\equiv 0(\text{mod } 8)$$ starting with a pair of extended equienergetic non regular graphs on $$8$$ vertices and also we construct a pair of extended equienergetic graphs on $$n$$ vertices for all $$n\geq 9$$ starting with a pair of equienergetic regular graphs on $$9$$ vertices.
Keywords: energy of a graph; extended energy of a graph; extended equienergetic graphs
Citation: Opuscula Math. 38, no. 1 (2018), 5-13, https://doi.org/10.7494/OpMath.2018.38.1.5
DOI: 10.7494/OpMath.2018.38.1.5
Issue No: Vol. 38, No. 1

• The spectrum problem for digraphs of order 4 and size 5

• Authors: Ryan C. Bunge, Steven DeShong, Saad I. El-Zanati, Alexander Fischer, Dan P. Roberts, Lawrence Teng
Pages: 15 - 30
Abstract: The paw graph consists of a triangle with a pendant edge attached to one of the three vertices. We obtain a multigraph by adding exactly one repeated edge to the paw. Now, let $$D$$ be a directed graph obtained by orientating the edges of that multigraph. For 12 of the 18 possibilities for $$D$$, we establish necessary and sufficient conditions on $$n$$ for the existence of a $$(K^{*}_{n},D)$$-design. Partial results are given for the remaining 6 possibilities for $$D$$.
Keywords: spectrum problem; digraph decompositions
Citation: Opuscula Math. 38, no. 1 (2018), 15-30, https://doi.org/10.7494/OpMath.2018.38.1.15
DOI: 10.7494/OpMath.2018.38.1.15
Issue No: Vol. 38, No. 1

• Existence of positive solutions to a discrete fractional boundary value
problem and corresponding Lyapunov-type inequalities

• Authors: Amar Chidouh, Delfim F. M. Torres
Pages: 31 - 40
Abstract: We prove existence of positive solutions to a boundary value problem depending on discrete fractional operators. Then, corresponding discrete fractional Lyapunov-type inequalities are obtained.
Keywords: fractional difference equations; Lyapunov-type inequalities; fractional boundary value problems; positive solutions
Citation: Opuscula Math. 38, no. 1 (2018), 31-40, https://doi.org/10.7494/OpMath.2018.38.1.31
DOI: 10.7494/OpMath.2018.38.1.31
Issue No: Vol. 38, No. 1

• Asymptotic profiles for a class of perturbed Burgers equations in one
space dimension

• Authors: F. Dkhil, M. A. Hamza, B. Mannoubi
Pages: 41 - 80
Abstract: In this article we consider the Burgers equation with some class of perturbations in one space dimension. Using various energy functionals in appropriate weighted Sobolev spaces rewritten in the variables $$\frac{\xi}{\sqrt\tau}$$ and $$\log\tau$$, we prove that the large time behavior of solutions is given by the self-similar solutions of the associated Burgers equation.
Keywords: Burgers equation; self-similar variables; asymptotic behavior; self-similar solutions
Citation: Opuscula Math. 38, no. 1 (2018), 41-80, https://doi.org/10.7494/OpMath.2018.38.1.41
DOI: 10.7494/OpMath.2018.38.1.41
Issue No: Vol. 38, No. 1

• Wiener index of strong product of graphs

• Authors: Iztok Peterin, Petra Žigert Pleteršek
Pages: 81 - 94
Abstract: The Wiener index of a connected graph $$G$$ is the sum of distances between all pairs of vertices of $$G$$. The strong product is one of the four most investigated graph products. In this paper the general formula for the Wiener index of the strong product of connected graphs is given. The formula can be simplified if both factors are graphs with the constant eccentricity. Consequently, closed formulas for the Wiener index of the strong product of a connected graph $$G$$ of constant eccentricity with a cycle are derived.
Keywords: Wiener index; graph product; strong product
Citation: Opuscula Math. 38, no. 1 (2018), 81-94, https://doi.org/10.7494/OpMath.2018.38.1.81
DOI: 10.7494/OpMath.2018.38.1.81
Issue No: Vol. 38, No. 1

• On the stability of some systems of exponential difference equations

• Authors: N. Psarros, G. Papaschinopoulos, C. J. Schinas
Pages: 95 - 115
Abstract: In this paper we prove the stability of the zero equilibria of two systems of difference equations of exponential type, which are some extensions of an one-dimensional biological model. The stability of these systems is investigated in the special case when one of the eigenvalues is equal to -1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. In addition, we study the existence and uniqueness of positive equilibria, the attractivity and the global asymptotic stability of these equilibria of some related systems of difference equations.
Keywords: difference equations; asymptotic behaviour; global stability; centre manifold; biological dynamics
Citation: Opuscula Math. 38, no. 1 (2018), 95-115, https://doi.org/10.7494/OpMath.2018.38.1.95
DOI: 10.7494/OpMath.2018.38.1.95
Issue No: Vol. 38, No. 1

• Study of ODE limit problems for reaction-diffusion equations

• Authors: Jacson Simsen, Mariza Stefanello Simsen, Aleksandra Zimmermann
Pages: 117 - 131
Abstract: In this work we study ODE limit problems for reaction-diffusion equations for large diffusion and we study the sensitivity of nonlinear ODEs with respect to initial conditions and exponent parameters. Moreover, we prove continuity of the flow and weak upper semicontinuity of a family of global attractors for reaction-diffusion equations with spatially variable exponents when the exponents go to 2 in $$L^{\infty}(\Omega)$$ and the diffusion coefficients go to infinity.
Keywords: ODE limit problems; shadow systems; reaction-diffusion equations; parabolic problems; variable exponents; attractors; upper semicontinuity
Citation: Opuscula Math. 38, no. 1 (2018), 117-131, https://doi.org/10.7494/OpMath.2018.38.1.117
DOI: 10.7494/OpMath.2018.38.1.117
Issue No: Vol. 38, No. 1

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