Applicable Analysis and Discrete Mathematics Vol. 9, No 1 (April, 2015)

Online version (ISSN 2406-100X) posted on April 3, 2015.

Printed version (ISSN 1452-8630) appeared on April 3, 2015.

• Title:

  Infinitely Many Equivalent Versions of the Graceful Tree Conjecture

  Authors:

  Tao-Ming Wang, Cheng-Chang Yang, Lih-Hsing Hsu, Eddie Cheng

  Classification:

  2000 Mathematical Subject Classification: 05C15, 05C78

  Keywords:

  Keywords and phrases: Graceful Tree Conjecture, Strongly Graceful Tree Conjecture, strongly graceful, gracefully similar, gracefully similar factor.

  Doi:

  DOI: 10.2298/AADM141009017W

  Download:

  Download

• Title:

  The linear (n-1)-arboricity of Cartesian product graphs

  Authors:

  Liancui Zuo, Shengjie He, Bing Xue

  Classification:

  2000 Mathematical Subject Classification: 05C15

  Keywords:

  Keywords and phrases: Linear k-forest, linear k-arboricity, Cartesian product graph, Hamming graph.

  Doi:

  DOI: 10.2298/AADM150202003Z

  Download:

  Download

• Title:

  ALPHA-KURAMOTO PARTITIONS FROM THE FRUSTRATED KURAMOTO MODEL GENERALISE EQUITABLE PARTITIONS

  Authors:

  Stephen Kirkland, Simone Severini

  Classification:

  2000 Mathematical Subject Classification: 5C90, 34D06

  Keywords:

  Keywords and phrases: Kuramoto model, phase synchronisation, graph partitions, systems of differential equations

  Doi:

  DOI: 10.2298/AADM141124018K

  Download:

  Download

• Title:

  On the Laplacian spectra of product graphs

  Authors:

  S. Barik, R. B. Bapat, S. Pati

  Classification:

  2000 Mathematical Subject Classification: 05C50, 05C76, 15A18

  Keywords:

  Keywords and phrases: Product graphs, Laplacian matrix, Laplacian eigenvalues, Characteristic set, Algebraic connectivity

  Doi:

  DOI: 10.2298/AADM150218006B

  Download:

  Download

• Title:

  On So's conjecture for integral circulant graphs

  Authors:

  J.W. Sander, T. Sander

  Classification:

  2000 Mathematical Subject Classification: 05C50, 11L03

  Keywords:

  Keywords and phrases: Cayley graph, Integral graph, Circulant graph, Graph spectrum, Multiplicative divisor set

  Doi:

  DOI: 10.2298/AADM150226009S

  Download:

  Download

• Title:

  Farey Lines defining Farey Diagrams and Application to some Discrete Structures

  Authors:

  Daniel Khoshnoudirad

  Classification:

  2000 Mathematical Subject Classification: 05A15, 05A16, 05C30, 11Y35

  Keywords:

  Keywords and phrases: Farey lines, enumerative combinatorics, graph theory in computer sciences, discrete planes, Diophantine equations

  Doi:

  DOI: 10.2298/AADM150219008K

  Download:

  Download

• Title:

  Dirichlet-to-Robin maps on finite networks

  Authors:

  Cristina Araúz, Ángeles Carmona, Andrés M. Encinas

  Classification:

  2000 Mathematical Subject Classification: 5C40, 05C50, 90B10, 94C15

  Keywords:

  Keywords and phrases: Finite networks, Schrödinger operator, Dirichlet-to-Robin map, Schur complement, Inverse problem

  Doi:

  DOI: 10.2298/AADM150207004A

  Download:

  Download

• Title:

  Blow-up for discrete Reaction-Diffusion Equations on Networks

  Authors:

  Soon-Yeong Chung, Jae-Hwang Lee

  Classification:

  2000 Mathematical Subject Classification: 39A12, 39A13, 39A70, 35K57

  Keywords:

  Keywords and phrases: Reaction-diffusion, Discrete Laplacian, Comparison principle, Blow-up

  Doi:

  DOI: 10.2298/AADM150210005C

  Download:

  Download

• Title:

  Two types of stability conditions for linear delay difference equations

  Authors:

  Jan Čermák, Jiří Jánský, Petr Tomášek

  Classification:

  2000 Mathematical Subject Classification: 39A30, 39A06

  Keywords:

  Keywords and phrases: Delay difference equation, asymptotic stability, characteristic polynomial

  Doi:

  DOI: 10.2298/AADM141009016C

  Download:

  Download

• Title:

  Analysis of Discrete Fractional Operators

  Authors:

  Ferhan M. Atıcı, Meltem Uyanik

  Classification:

  2000 Mathematical Subject Classification: 26A33, 39A12, 39A70

  Keywords:

  Keywords and phrases: Discrete fractional calculus, forward fractional difference operator

  Doi:

  DOI: 10.2298/AADM150218007A

  Download:

  Download

• Title:

  Existence of solutions for hybrid fractional pantograph equations

  Authors:

  Mohamed Abdalla Darwish, Kishin Sadarangani

  Classification:

  2000 Mathematical Subject Classification: 45G10, 45M99, 47H09

  Keywords:

  Keywords and phrases: Banach algebras, hybrid, measure of noncompactness, Riemann-Liouville, pantograph equations

  Doi:

  DOI: 10.2298/AADM150126002D

  Download:

  Download

• Title:

  NORM INEQUALITIES FOR NEW CONVOLUTIONS AND THEIR APPLICATIONS

  Authors:

  Dinh Thanh Duc, Nguyen Du Vi Nhan

  Classification:

  2000 Mathematical Subject Classification: 26D10, 26D15, 44A35

  Keywords:

  Keywords and phrases: Hölder's inequality, convolution, integral transform, boundedness, differential equation, Lp-weighted estimate

  Doi:

  DOI: 10.2298/AADM150109001D

  Download:

  Download

• Title:

  Complete Solution to Seven-point Schemes of Discrete Anisotropic Laplacian on Regular Hexagons

  Authors:

  Daniel Lee

  Classification:

  2000 Mathematical Subject Classification: 65N06, 35J05, 15A06

  Keywords:

  Keywords and phrases: Compact scheme, Hexagonal finite volume, Seven-point method, Anisotropic Laplacian

  Doi:

  DOI: 10.2298/AADM150310010L

  Download:

  Download