Yazar "Das, Kinkar Chandra" seçeneğine göre listele

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    A new graph based on the semi-direct product of some monoids
    (SPRINGER INTERNATIONAL PUBLISHING AG, 2013) Karpuz, Eylem Guzel; Das, Kinkar Chandra; Cangul, Ismail Naci; Cevik, Ahmet Sinan
    In this paper, firstly, we define a new graph based on the semi-direct product of a free abelian monoid of rank n by a finite cyclic monoid, and then discuss some graph properties on this new graph, namely diameter, maximum and minimum degrees, girth, degree sequence and irregularity index, domination number, chromatic number, clique number of Gamma (P-M). Since graph theoretical studies (including such above graph parameters) consist of some fixed point techniques, they have been applied in fields such as chemistry (in the meaning of atoms, molecules, energy etc.) and engineering (in the meaning of signal processing etc.), game theory and physics.
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    On the spectral radius of bipartite graphs which are nearly complete
    (SPRINGEROPEN, 2013) Das, Kinkar Chandra; Cangul, Ismail Naci; Maden, Ayse Dilek; Cevik, Ahmet Sinan
    For p, q, r, s, t is an element of Z(+) with rt <= p and st <= q, let G = G(p, q; r, s; t) be the bipartite graph with partite sets U = {u(1), ..., u(p)} and V = {v(1),..., v(q)} such that any two edges u(i) and v(j) are not adjacent if and only if there exists a positive integer k with 1 <= k <= t such that (k - 1) r + 1 <= i <= kr and (k - 1) s + 1 <= j <= ks. Under these circumstances, Chen et al. (Linear Algebra Appl. 432: 606-614, 2010) presented the following conjecture: Assume that p <= q, k < p, vertical bar U vertical bar = p, vertical bar V vertical bar = q and vertical bar E(G)vertical bar = pq - k. Then whether it is true that lambda(1)(G) <= lambda(1)(G(p, q; k, 1; 1)) = root pq - k + root p(2)q(2) - 6pqk + 4pk + 4qk(2) - 3k(2)/2. In this paper, we prove this conjecture for the range min(vh is an element of V){deg v(h)} <= left perpendicular p-1/2right perpendicular.
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    Some array polynomials over special monoid presentations
    (SPRINGER INTERNATIONAL PUBLISHING AG, 2013) Cevik, Ahmet Sinan; Das, Kinkar Chandra; Simsek, Yilmaz; Cangul, Ismail Naci
    In a recent joint paper (Cevik et al. in Hacet. J. Math. Stat., acceptted), the authors have investigated the p-Cockcroft property (or, equivalently, efficiency) for a presentation, say , of the semi-direct product of a free abelian monoid rank two by a finite cyclic monoid. Moreover, they have presented sufficient conditions on a special case for to be minimal whilst it is inefficient. In this paper, by considering these results, we first show that the presentations of the form can actually be represented by characteristic polynomials. After that, some connections between representative characteristic polynomials and generating functions in terms of array polynomials over the presentation will be pointed out. Through indicated connections, the existence of an equivalence among each generating function in itself is claimed studied in this paper. MSC: 11B68, 11S40, 12D10, 20M05, 20M50, 26C05, 26C10.