International Journal of Discrete Mathematics

Volume 1, Issue 1, December 2016

  • The PI(Padmakar-Ivan) Index of Polyominoes

    P. Gayathri, K. R. Subramanian

    Issue: Volume 1, Issue 1, December 2016
    Pages: 1-4
    Received: Sep. 19, 2016
    Accepted: Nov. 18, 2016
    Published: Dec. 26, 2016
    DOI: 10.11648/j.dmath.20160101.11
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    Abstract: The Padmakar – Ivan (PI) index of polyominoes is examined.Efficient calculations of formulas for PI index for the polyominoes are put forward. In chemical graph theory, the PI index is a topological indexof a graph G is defined as , where for edge e = xy, n1 (e) is the number of edges of G lying closer to x than y, n2 (e) is the number of edges of ... Show More
  • Solution of a Parabolic Partial Differential Equation on Digital Spaces: A Klein Bottle, a Projective Plane, a 4D Sphere and a Moebius Band

    Alexander V. Evako

    Issue: Volume 1, Issue 1, December 2016
    Pages: 5-14
    Received: Oct. 08, 2016
    Accepted: Nov. 17, 2016
    Published: Dec. 27, 2016
    DOI: 10.11648/j.dmath.20160101.12
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    Abstract: This paper studies a parabolic partial differential equation on digital spaces and digital n-dimensional manifolds, which are digital models of continuous n-manifolds. Conditions for the existence of solutions of equations are determined and investigated. Numerical solutions of the equation on a Klein bottle, a projective plane, a 4D sphere and a M... Show More
  • The Theorem of Cayley and Γ Matrices

    Xiao-Yan Gu, Jian-Qiang Sun

    Issue: Volume 1, Issue 1, December 2016
    Pages: 15-19
    Received: Oct. 31, 2016
    Accepted: Nov. 17, 2016
    Published: Dec. 27, 2016
    DOI: 10.11648/j.dmath.20160101.13
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    Abstract: In this article, the connections between symmetric groups and the matrix groups are investigated for exploring the application of Cayley’s theorem in finite group theory. The exact forms of the permutation groups isomorphic to the groups , and are obtained within the frame of the group-theoretical approach. The results are analyzed in detail and compared with that from Cayley's theorem. It shows that the orders of the symmetric groups in present formulas are less than the latter. Various directions for future investigations on the research results have been pointed out.
  • An Analytic Approach to Weakly-Singular Integro-Dynamic Equation on Time Scales

    Adil Mısır

    Issue: Volume 1, Issue 1, December 2016
    Pages: 20-29
    Received: Dec. 12, 2016
    Accepted: Dec. 22, 2016
    Published: Jan. 16, 2017
    DOI: 10.11648/j.dmath.20160101.14
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    Abstract: In this paper, we present a new and simple approach to resolve linear and nonlinear weakly-singular Volterra integro-dynamic equations of first and second order on any time scales. In order to eliminate the singularity of the equation, nabla derivative is used and then transforming the given first-order integro-dynamic equations onto an first-order... Show More
  • Algorithm of Search of Large Prime Numbers

    Kochkarev Bagram Sibgatullovich

    Issue: Volume 1, Issue 1, December 2016
    Pages: 30-32
    Received: Dec. 03, 2016
    Accepted: Dec. 22, 2016
    Published: Jan. 17, 2017
    DOI: 10.11648/j.dmath.20160101.15
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    Abstract: The large number of problems in the theory of the numbers possessing one characteristic sign called by us binary mathematical statements from the natural parameter which in the time of Pythagoras and Euclid still aren’t solved was prompted to us that the reason of such situation should be looked for in the mathematics bases. We have entered concept... Show More