1. Moo Young Sohn, Title: A characterization of planar graphs with small diameter. Abstract: The graphs that arise from such physical networks are usually planar. An important applications of planar graphs is in designing and construction of electrical circuits. So it is sometimes important to minimize the amount of nonplanarity. Planar graphs with small diameter are often important in applications. What is the characterization of regular planar graphs with diameter 2? In this talk, We shall deal with the problem of chracterization of regular planar graph with diameter two by using elementary method. 2. Changwoo Lee, Title: The Expected Independent Domination Number of a Random Recursive Tree Abstract: We derive a formula for the expected value of the independent domination number of a random recursive tree with n vertices and show that the independent domination number of almost every recursive tree with vertices is quite close to. 3. Sang-Gu Lee, Title: The Binet Formula and Representations of $k$-generalized Fibonacci Numbers Abstract: We will consider a generalization of Fibonacci sequence, which is called the k-generalized Fibonacci sequence for positive integer k >= 2. In this lecture, we will derive a generalized Binet formula for the k-generalized Fibonacci sequence by using the determinant and we give several combinatorial representations of k-generalized Fibonacci numbers. This include five different representations of k-generalized Fibonacci sequence. 4. Sangwook Ree, Title : On Bipartite Tournament Matrices Abstract: A tournament is the record of a round-robin competition between players. It is combinatorially interesting and represented by a digraph whose adjacency matrix is called a tournament matrix. Tournament matrices enjoy many interesting combinatorial properties. They can be studied combinatorial matrix theoretically as well as graph theoretically. By grouping players to teams, we get a generalization of tournaments and tournament matrices, which we call respectively multipartite tournaments and multipartite toutnament matrices. We look at the spectral bounds of bipartite tournament matrices, that is, tournament matrices of two teams, with arbitrary team size. We see when bipartite matrices exist and how players and teams of the matrices are evenly ranked. We show that a bipartite tournament matrix can be both regular and normal when and only when it has the same team size. We also find the condition for the variance of the Perron vector of the bipartite tournament matrix to vanish. 5. Sungchul Lee, Title : The construction of minimal spanning tree and the strong limit laws. Abstract : Let K_n be the complete graph with vertex set and edge set . For each edge $e$ in $E_n$ we attach an weight $U(e)$ where $\{U(e):e\in E_n\}$ are iid uniform random variables on the unit interval $[0,1]$. A minimal spanning tree on $K_n$ is a spanning tree $T_n$ on $V_n$ such that $\sum_{e \in T_n} U(e) = \min \{ \sum_{e \in T} U(e) : T \mbox{ a spanning tree on $V_n$} \}$. In this talk we establish the large deviation for the length, the number of vertices of degree $\al$, the number of edges of ${\cal T}(K_n)$ with weight at most $t/n$, by introducing a new algorithm for the construction of minimal spanning tree and estimating the corresponding moment generating function, and hence obtain the strong limit laws. 6. Chung-Nim Lee, Title : Counting Geodesic Paths in the n-Dimensional Digital Space Abstract :Between two points of the n-dimensional euclidean space, there is a unique geodesic path. However there are n different geodesic paths in the discrete space of n dimensional digital space depending on the possible n different metric functions. We address the problem of counting the number of geodesic paths between two given points in each metric function. This problem has been solved by works by Rosenfeld and his colleagues for dimension two, and Goh and his colleagues for dimension three. Applications are found in digital image processing. 7. Junho Song, Title : An Asymptotic Formula for $\exp(\frac{x}{1-x})$ Abstract : We show that $G(x)=e^{x/(1-x)}-1$ is the exponential generating function for the labeled digraphs whose weak components are transitive tournaments and derive both a recursive formula and an explicit formula for the number of them on $n$ vertices. Moreover, we investigate the asymptotic behavior for the coefficients of $G(x)$ using Hayman's method. 8. Jin Ho Kwak, Title : Combinatorial Versions of Hurwitz Classification Theorem for Branched Surface Coverings and Related Enumeration Problems Abstract : In this talk, we aim to give new versions of Hurwitz Theorems for the classification and the existence of branched surface coverings and also to give new combinatorial proofs of them. As results, we can drive several enumeration formulas for some kinds of branched surface coverings, like as regular coverings. For example, The number of nonisomorphic $n$-fold branched coverings of a given closed surface can be determined by the number of nonisomorphic $n$-fold unbranched coverings of the surface and the number of nonisomorphic $n$-fold graph coverings of a suitable bouquet of circles. The same thing is also true for regular branched coverings. Some explicit enumeration of them are also possible. 9. Suk-Geun Hwang, Title : Genaralized Hessenberg matrices and expansion of bipartite graphs Abstract : Genelized Hessenberg matrices are those (0,1)-matrices which are incidence matrices of bipartite fraphs obtained from the connected graph with exactly one edge on two vertices by so called successive copying rows or columns. In this talk we discuss about a new metod of constructing generalized Hessenberg matrices by graph theoretical means, and investigate some properties of combinatorial concepts in connection with generalized Hessenberg matrices. 10. Sung-Yell Song Title: Enumeration of certain biological codes Abstract : We count the spanning time for certain abstract biological codes by using the methods of generating functions and recursion. We derive several enumeration formulas. 11. Hyun Kwang Kim Title: On Regular Polytope Numbers Abstract : A classical theorem of Lagrange says that every natural number can be written as a sum of four squares. We can generalize this beautiful result in two ways. The one way is a horizontal generalization (Cauchy's polygonal number theorem) which says that every natural number can be written as a sum of k k-gonal numbers. The other way is a vertical generalization (Hilbert-Waring problem) which states that every natural number can be written as a sum of 4 squares, 9 cubes, 19 fourth powers, 37 fifth powers,and so on. In this talk we shall consider a horizontal generalization of Hilbert-Waring problem, or equivalently, a vertical generalization of Cauchy's polygonal number theorem. More precisely, we shall associate to each regular polytope a sequence of natural numbers which we shall call regular polytope numbers, and consider the problem of expressing natural number as a sum of regular polytope numbers. The way of construting regular polytope numbers as well as numerical data will be presented. 12. Sungpyo Hong Title : Bipartite graph bundles with connected fibers Abstract : The isomorphism classes of graph bundles and graph coverings over a finite connected simple graph G have been enumerated by Kwak and Lee. Recently, Archdeacon, at al, characterized bipartite coverings of G and enumerated the isomorphism classes of regular 2p-fold bipartite coverings of G, when G is nonbipartite. In this talk, we characterize bipartite graph bundles over G and derive some enumeration formulas of the isomorphism classes of them when the fiber is a connected bipartite graph. As an application, we compute the exact numbers of the isomorphism classes of bipartite graph bundles over G when the fiber is the path P_n or the cycle C_n. 13. Suh-Ryung Kim Title: On graph inquality $\theta(G^m) \leq \theta(G)$ Abstract : In this talk, we present some results on the graph inequality $\theta (G^m) \leq \theta(G)$ where $\theta(G)$ is the edge clique cover number of a graph $G$. We show that any graph $G$ with at most $\theta(G)$ vertices satisfies $\theta (G^2) \leq \theta(G)$. Among the graphs with more than $\theta (G)$ vertices, we find some chordal graphs violating the inequality and show that dually chordal graphs and power-chordal graphs satisfy the inequality. We show that $\theta(G^{2l+1}) \leq \theta(G)$ for any simple graph $G$ and construct a graph not satisfying $\theta(G^{2l}) \leq \theta(G)$. We also give an exact formula computing $\theta (T^m)$ for a tree $T$. 14. Han Hyuk Cho Title: Perfect minus dominations and public key systems Abstract : Finding perfect minus domination is a NP-complete problem, and its application to cryptosystem is an interesting application. Finding perfect minus domination is related to finding a pair of disjoint perfect dominations. In this paper, we consider the perfect minus domination in cubic graph, and the public key crypto-system related to the perfect minus domination. We also consider the possible key attack and message attack related to the crypto-system. 15. Jaeun Lee Title: Distributions of regular branched surface coverings Abstract : For the question: In how many different ways can a given surface be a branched covering of another given surface, there are several partial answers by Kwak, Lee et al: enumerating the equivalence classes of regular branched prime-fold coverings of surfaces, and under the condition that the covering transformation group is the dihedral group, or the direct sum of m copies of the cyclic group of order prime. Recently, Kwak et al. enumerated the number of equivalence classes of branched orientable A-coverings of an nonorientable surface, but the covering surface is not specified when the covering transformation group A is a finite abelian group. In this talk, we apply Jones's result to determine the distribution of the branched A-coverings of an orientable surface when A is any finite group. As the main result of this paper, we extend this work to determine the distribution of the branched A-coverings of any nonorientable surface when A is any finite group. 16. Yoomi Rho, Title : An Extremal Problem concerning Graphs not containing $K_t$ and $K_{t,t}$ Abstract : We consider the following problem. Let $t$ and $n$ be positive integers with $n\geq t\geq 2$. Determine the maximum number of edges of a graph of order $n$ that contains neither $K_t$ nor $K_{t,t}$ as a subgraph. For $n<2t$, it is solved by Tur\'{a}n's theorem and for $n=2t$, by Brualdi and Mellendorf. We solve it for $n=2t+1$. 17. Vince Grolmusz Title: Constructing Set-Systems with Prescribed Intersection Sizes Abstract: Let $f$ be an $n$ variable polynomial with positive integer coefficients, and let ${\cal H}=\{H_1,H_2,\ldots,H_m\}$ be a set-system on the $n$-element universe. We define set-system $f({\cal H})=\{G_1,G_2,\ldots,G_m\}$, and prove that $f(H_{i1}\cap H_{i2}\cap\ldots\cap H_{ik})=|G_{i1}\cap G_{i2}\cap\ldots\cap G_{ik}|$, for any $1\leq k\leq m$, where $f(H_{i1}\cap H_{i2}\cap\ldots\cap H_{ik})$ denotes the value of $f$ on the characteristic vector of $H_{i1}\cap H_{i2}\cap\ldots\cap H_{ik}$. The construction of $f({\cal H})$ is a straightforward polynomial--time algorithm from ${\cal H}$ and polynomial $f$. In this paper we use this algorithm for constructing set-systems with prescribed intersection sizes modulo an integer. As a by-product of our method, some Ray-Chaudhuri--Wilson-like theorems are proved. 18. Mikl\'os Ruszink\'o Title: Superimposed codes by Ruszinko et. al. Abstract: A family of subsets of an $n$-set is a binary superimposed code if no set is covered by the union of $r$ others. We will discuss the extremal properties of such families in binary regular and non-regular cases. We will also show the connections of these codes to distributed computing. Th geometric version of this problem will be also investigated. Most of the results were obtained jointly with Zolt\'an F\"uredi. 19. Andr\'as Luk\'acs Title: Concepts for strong negative dependence of several binary-valued random variables Abstract: In the talk some concept of mutual negative dependence of binary-valued random variables are considered. These properties are enhancement of the pairwise negative correlations of random variables. The main concepts are the usual negative association and the van den Berg-Kesten property, both a possible counterpart of the positive association (FKG inequality). Examples, counter-examples, and conjectures are presented.