http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2013 , Hindawi Publishing Corporation . All rights reserved. Thu, 13 Jun 2013 09:28:16 +0000 http://www.hindawi.com/journals/jdm/2013/857908/ The terminal Hosoya polynomial of a graph is defined as , where is the number of pairs of pendant vertices of that are at distance . In this paper we obtain terminal Hosoya polynomial of line graphs. H. S. Ramane, A. B. Ganagi, K. P. Narayankar, and S. S. Shirkol Copyright © 2013 H. S. Ramane et al. All rights reserved. Mon, 15 Apr 2013 14:17:01 +0000 http://www.hindawi.com/journals/jdm/2013/219291/ Closure properties of some classes of right infinite words have been studied extensively; we are interested in the general algebraic structure of right infinite words. We investigate preorder of morphism invariant classes and show that it is not a semilattice. Liga Kulesa Copyright © 2013 Liga Kulesa. All rights reserved. Sun, 14 Apr 2013 08:45:07 +0000 http://www.hindawi.com/journals/jdm/2013/721051/ A decomposition of a graph is a collection of edge-disjoint subgraphs of such that every edge of belongs to exactly one . If each is a path or a cycle in , then is called a path decomposition of . If each is a path in , then is called an acyclic path decomposition of . The minimum cardinality of a path decomposition (acyclic path decomposition) of is called the path decomposition number (acyclic path decomposition number) of and is denoted by () (()). In this paper we initiate a study of the parameter and determine the value of for some standard graphs. Further, we obtain some bounds for and characterize graphs attaining the bounds. We also prove that the difference between the parameters and can be made arbitrarily large. S. Arumugam, I. Sahul Hamid, and V. M. Abraham Copyright © 2013 S. Arumugam et al. All rights reserved. Sun, 31 Mar 2013 13:56:48 +0000 http://www.hindawi.com/journals/jdm/2013/808105/ A vertex-deleted subgraph of a graph is called a card of . A card of with which the degree of the deleted vertex is also given is called a degree associated card (or dacard) of . The degree associated reconstruction number drn () of a graph is the size of the smallest collection of dacards of that uniquely determines . The adversary degree associated reconstruction number of a graph , adrn(), is the minimum number such that every collection of dacards of that uniquely determines . In this paper, we show that adrn of wheels and complete bipartite graphs on at least 4 vertices is 2 or 3. S. Monikandan, S. Sundar Raj, C. Jayasekaran, and A. P. Santhakumaran Copyright © 2013 S. Monikandan et al. All rights reserved. Mon, 25 Mar 2013 08:24:56 +0000 http://www.hindawi.com/journals/jdm/2013/491627/ The function where is the logarithm integral and the number of primes up to is well known to be positive up to the (very large) Skewes' number. Likewise, according to Robin's work, the functions and , where and are Chebyshev summatory functions, are positive if and only if Riemann hypothesis (RH) holds. One introduces the jump function at primes and one investigates , , and . In particular, , and for . Besides, for any odd , an infinite set of the so-called Chebyshev primes. In the context of RH, we introduce the so-called Riemann primes as champions of the function (or of the function ). Finally, we find a good prime counting function , that is found to be much better than the standard Riemann prime counting function. Michel Planat and Patrick Solé Copyright © 2013 Michel Planat and Patrick Solé. All rights reserved. Wed, 20 Mar 2013 18:22:29 +0000 http://www.hindawi.com/journals/jdm/2013/450481/ We introduce a -deformation of the Yang and Youn matrix approach for Appell polynomials. This will lead to a powerful machinery for producing new and old formulas for -Appell polynomials, and in particular for -Bernoulli and -Euler polynomials. Furthermore, the --polynomial, anticipated by Ward, can be expressed as a sum of products of -Bernoulli and -Euler polynomials. The pseudo -Appell polynomials, which are first presented in this paper, enable multiple -analogues of the Yang and Youn formulas. The generalized -Pascal functional matrix, the -Wronskian vector of a function, and the vector of -Appell polynomials together with the -deformed matrix multiplication from the authors recent article are the main ingredients in the process. Beyond these results, we give a characterization of -Appell numbers, improving on Al-Salam 1967. Finally, we find a -difference equation for the -Appell polynomial of degree . Thomas Ernst Copyright © 2013 Thomas Ernst. All rights reserved. Wed, 20 Mar 2013 14:11:40 +0000 http://www.hindawi.com/journals/jdm/2013/734836/ In this paper, using the production matrix of a Riordan array, we obtain a recurrence relation for polynomial sequence associated with the Riordan array, and we also show that the general term for the sequence can be expressed as the characteristic polynomial of the principal submatrix of the production matrix. As applications, a unified determinant expression for the four kinds of Chebyshev polynomials is given. Sheng-liang Yang and Sai-nan Zheng Copyright © 2013 Sheng-liang Yang and Sai-nan Zheng. All rights reserved. Wed, 20 Mar 2013 08:35:05 +0000 http://www.hindawi.com/journals/jdm/2013/587196/ Let be a simple graph. A set is a dominating set of , if every vertex in is adjacent to at least one vertex in . We denote the family of dominating sets of a graph with cardinality by . In this paper we introduce graphs with specific constructions, which are denoted by . We construct the dominating sets of by dominating sets of graphs , , and . As an example of , we consider . As a consequence, we obtain the recursive formula for the number of dominating sets of . Saeid Alikhani and Yee-Hock Peng Copyright © 2013 Saeid Alikhani and Yee-Hock Peng. All rights reserved. Wed, 13 Mar 2013 10:25:07 +0000 http://www.hindawi.com/journals/jdm/2013/628952/ An ()-arc is a set of n points of a projective plane such that some r, but no of them, are collinear. The maximum size of an ()-arc in PG(2, q) is denoted by (2, q). In this paper, a new (286, 16)-arc in PG(2,19), a new (341, 15)-arc, and a (388, 17)-arc in PG(2,25) are constructed, as well as a (394, 16)-arc, a (501, 20)-arc, and a (532, 21)-arc in PG(2,27). Tables with lower and upper bounds on (2, 25) and (2, 27) are presented as well. The results are obtained by nonexhaustive local computer search. Rumen Daskalov and Elena Metodieva Copyright © 2013 Rumen Daskalov and Elena Metodieva. All rights reserved. Tue, 12 Mar 2013 08:01:30 +0000 http://www.hindawi.com/journals/jdm/2013/983830/ We define m-HPK-residual graphs in which HPK is a hyperplane complete graph. We extend P. Erdös, F. Harary, and M. Klawe's definition of plane complete residual graph to hyperplane and obtain the hyperplane complete residual graph. Further, we obtain the minimum order of HPK-residual graphs and m-HPK-residual graphs. In addition, we obtain a unique minimal HPK-residual graphs and a unique minimal m-HPK-residual graphs. Huiming Duan and Yonghong Li Copyright © 2013 Huiming Duan and Yonghong Li. All rights reserved. Mon, 25 Feb 2013 10:11:21 +0000 http://www.hindawi.com/journals/jdm/2013/170263/ We consider an iterative algorithm for solving a complex matrix equation with conjugate and transpose of two unknowns of the form: + . With the iterative algorithm, the existence of a solution of this matrix equation can be determined automatically. When this matrix equation is consistent, for any initial matrices , the solutions can be obtained by iterative algorithm within finite iterative steps in the absence of round-off errors. Some lemmas and theorems are stated and proved where the iterative solutions are obtained. A numerical example is given to illustrate the effectiveness of the proposed method and to support the theoretical results of this paper. Mohamed A. Ramadan, Talaat S. El-Danaf, and Ahmed M. E. Bayoumi Copyright © 2013 Mohamed A. Ramadan et al. All rights reserved. Wed, 20 Feb 2013 08:09:44 +0000 http://www.hindawi.com/journals/jdm/2013/892839/ Let be a nontrivial, simple, finite, connected, and undirected graph. A graphoidal decomposition (GD) of is a collection of nontrivial paths and cycles in that are internally disjoint such that every edge of lies in exactly one member of . By restricting the members of a GD to be induced, the concept of induced graphoidal decomposition (IGD) of a graph has been defined. The minimum cardinality of an IGD of a graph is called the induced graphoidal decomposition number and is denoted by (). An IGD of without any cycles is called an induced acyclic graphoidal decomposition (IAGD) of , and the minimum cardinality of an IAGD of is called the induced acyclic graphoidal decomposition number of , denoted by (). In this paper we determine the value of () and () when is a product graph, the factors being paths/cycles. Mayamma Joseph and I. Sahul Hamid Copyright © 2013 Mayamma Joseph and I. Sahul Hamid. All rights reserved. Thu, 07 Feb 2013 12:28:55 +0000 http://www.hindawi.com/journals/jdm/2013/625912/ Singleton-type upper bounds on the minimum Lee distance of general (not necessarily linear) Lee codes over are discussed. Two bounds known for linear codes are shown to also hold in the general case, and several new bounds are established. Codes meeting these bounds are investigated and in some cases characterised. Tim L. Alderson and Svenja Huntemann Copyright © 2013 Tim L. Alderson and Svenja Huntemann. All rights reserved. Wed, 30 Jan 2013 11:45:18 +0000 http://www.hindawi.com/journals/jdm/2013/373927/ We investigate sums of products of Cauchy numbers including poly-Cauchy numbers: . A relation among these sums shown in the paper and explicit expressions of sums of two and three products (the case of and that of described in the paper) are given. We also study the other three types of sums of products related to the Cauchy numbers of both kinds and the poly-Cauchy numbers of both kinds. Takao Komatsu Copyright © 2013 Takao Komatsu. All rights reserved. Thu, 10 Jan 2013 18:03:28 +0000 http://www.hindawi.com/journals/jdm/2013/140537/ We construct (0, 2)-graphs from root systems with simply laced diagram and study their properties. Andries E. Brouwer and Leonard Chastkofsky Copyright © 2013 Andries E. Brouwer and Leonard Chastkofsky. All rights reserved. Thu, 10 Jan 2013 14:44:09 +0000 http://www.hindawi.com/journals/jdm/2013/692645/ This paper proposes a new proof of Dilworth's theorem. The proof is based upon the minflow/maxcut property in flow networks. In relation to this proof, a new method to find both a Dilworth decomposition and a maximal antichain is presented. Wim Pijls and Rob Potharst Copyright © 2013 Wim Pijls and Rob Potharst. All rights reserved. Tue, 08 Jan 2013 09:45:36 +0000 http://www.hindawi.com/journals/jdm/2013/851751/ This paper refers to the algorithmic transformation of a meander to its uniquely defined compression. We obtain this directly from meandric permutations, thus creating representations of large classes of meanders of different orders. We prove basic properties, give arithmetic results, and produce generating procedures. A. Panayotopoulos and P. Vlamos Copyright © 2013 A. Panayotopoulos and P. Vlamos. All rights reserved. Thu, 03 Jan 2013 15:50:31 +0000 http://www.hindawi.com/journals/jdm/2013/105624/ The signless Laplacian polynomial of a graph is the characteristic polynomial of the matrix , where is the diagonal degree matrix and is the adjacency matrix of . In this paper we express the signless Laplacian polynomial in terms of the characteristic polynomial of the induced subgraphs, and, for regular graph, the signless Laplacian polynomial is expressed in terms of the derivatives of the characteristic polynomial. Using this we obtain the characteristic polynomial of line graph and subdivision graph in terms of the characteristic polynomial of induced subgraphs. Harishchandra S. Ramane, Shaila B. Gudimani, and Sumedha S. Shinde Copyright © 2013 Harishchandra S. Ramane et al. All rights reserved.