
Call for Papers
We selected "Combinatorial Matrix Theory and its applications" as the main theme of the special session 8 in the 2009 Joint Meeting of the KMS and the AMS. This session will focus on crosscutting researches and practices in combinatorial matrix theories and various applications. This theme will be divided into some primary topics for science and engineering research in today's world; Life, Internet Infrastructure, Engineering, Energy, and Natural Resources.
This session will be composed of oral talks and a poster presentations. Oral talks will be held for the presentation of selected papers and panel discussions. Every talks will be composed of highranking officials from policymaking organizations and researchers from both Korea and the United States. This session is currently soliciting papers. We particularly welcome papers that cut across multiple disciplines. It is expected that some selected papers could serve as an excellent basis for special publications of various journals. The special session 8 : "Combinatorial Matrix Theory" would like to entertain proposals for some special publications.
Submission Complete!
Special Session on Combinatorial Matrix
Theory (Code: SS 8A)
Online Submission (Closed)  Tentative Program
First Joint International Meeting of the AMS and the Korean Mathematical
Society Seoul, South Korea, December 1620, 2009 (Wednesday 
Sunday) Meeting #1055
Tentative Program Schedule (This schedule is tentative so, it should be modified.)
 Friday, December 18, 2009, 8:30 a.m  10:50 a.m.
Special Session on Combinatorial Matrix Theory (Code: SS8A)
Room [TBA], Ehwa Women University Organizers of this session: SukGeun
Hwang, Kyungpook National University sghwang@knu.ac.kr Bryan Shader, University of Wyoming, bshader@uwyo.edu Chair: SukGeun
Hwang, Kyungpook National University sghwang@knu.ac.kr
 8:30 a.m.
Totally Nonnegative (
0,1)Matrices Richard A. Brualdi*, WISC, brualdi@math.wisc.edu
Abstract: TBA (KMS submission)
Abstract Number :
SSA81019191044
 9:00 a.m.
The Rules of Divisiblity for
Matrices Ivo Herzog*, OSU, herzog.23@osu.edu
Abstract: TBA (KMS submission)
Abstract Number :
SSA81019191147
 9:30 a.m.
Characterizations of termrank
preservers SeokZun Song*, Jeju National
University, szsong@jejunu.ac.kr
Abstract: TBA (KMS submission)
Abstract Number : SSA81019191254
 10:00 a.m.
Infinite Families of Recursive Formulas
Generating Power Moments of Ternary Kloosterman Sums with Square Arguments
Associated with O^(2n,q) Dae San Kim*,
Sogang University, dskim@sogang.ac.kr
Abstract: In this paper, we construct eight
infinite families of ternary linear codes associated with double cosets with
respect to certain maximal parabolic subgroup of the special orthogonal group
$SO^{}(2n,q)$. Here ${q}$ is a power of three. Then we obtain four infinite
families of recursive formulas for power moments of Kloosterman sums with square
arguments and four infinite families of recursive formulas for even power
moments of those in terms of the frequencies of weights in the codes. This is
done via Pless power moment identity and by utilizing the explicit expressions
of exponential sums over those double cosets related to the evaluations of
$\lq\lq$Gauss sums" for the orthogonal groups $O^{}(2n,q)$.
Abstract
Number : SSA8918141716
 10:30 a.m.
Simultaneous LyapunovSylvester equations for
matrices QuocPhong Vu*, Ohio University, vu@ohio.edu SangGu Lee, Sungkyunkwan
University
Abstract: We
investigate simultaneous solutions of the matrix equations $A_iXXB_i=C_i,
i=1,2,...,k$, where $\{A_i\}$ and $\{B_i\}, i=1,2,...k,$ are commuting ktuples.
We prove that if the joints spectra of the ktuples $\{A_i\}$ and $\{B_i\} are
disjoint, then the equations have a unique common matrix solution for every
ktupple $\{C_i\}, i=1,...,k$ (under some natural compatibility condition on
$C_i$) and, conversely, if for every such ktuple ${C_i}, i=1,...,k$, the
equations have a unique common solution, then the joint spectra of the ktuples
$\{A_i\}$ and $\{B_i\} are disjoint. The results are natural extensions of the
classical result on single matrix LyapunovSylvester
equation.
Abstract Number : SSA8930164946
 Saturday, December 19, 2009, 8:30 a.m  10:50 a.m.
Special Session on Combinatorial Matrix Theory (Code: SS8A)
Room [TBA], Ehwa Women University Organizers of this session: SukGeun
Hwang, Kyungpook National University sghwang@knu.ac.kr Bryan Shader, University of Wyoming, bshader@uwyo.edu Chair: Bryan Shader, University of Wyoming, bshader@uwyo.edu
 8:30 a.m.
On graphs with smallest eigenvalue
3 Jack Koolen*, POSTECH, koolen@postech.ac.kr Hye Jin
Jang
Abstract: In 1976
Cameron et all showed that essentially all graphs with smallest eigenvalue at
least 2 are generalized line graphs. In this talk I discuss graphs with
smallest eigenvalue at least 3. In particular, I will show that these graphs
behave quite a bit different then those with smallest eigenvalue at least 2.
Abstract Number : SSA81013114322
 9:00 a.m.
Eigenvalues and connectivity of regular
graphs Sebastian M. Cioaba*, University of
Delaware, USA, cioaba@math.udel.edu
Abstract: In this talk, I will discuss some old
and new results relating the connectivity of a regular graph to its eigenvalues.
Abstract Number : SSA8924004258
 9:30 a.m.
On the largest eigenvalues of bipartite graphs
which are nearly complete InJae Kim*,
Minnesota State University, Mankato, injae.kim@mnsu.edu YiFan Chen, HungLin Fu,
National Chiao Tung University, Eryn Stehr, Minnesota State University, Mankato,
Bredon Watts, University of Oklahoma, Norman
Abstract: The topological structure of a graph,
consisting of vertices and edges, can be described in an algebraic object such
as the $(0,1)$ adjacency matrix of the graph. It is well known that spectral
properties of the adjacency matrix of a graph are closely related to its graph
theoretic properties. We even say that the eigenvalues of the adjacency matrix
of the graph are the eigenvalues of the graph. In this talk some results on the
largest eigenvalues of bipartite graphs are presented. We first compute the
largest eigenvalues of a specific class of bipartite graphs which are nearly
complete, and then list nearly complete bipartite graphs according to the
magnitudes of their largest eigenvalues. These results are related to a
conjecture in [A. Bhattacharya, S. Friedland and U.N. Peled, On the first
eigenvalue of bipartite graphs, \emph{Electronic Journal of Combinatorics} 15
(2008) $\#$R144].
Abstract Number : SSA8921221534
 10:00 a.m.
On conjectures involving Laplacian eigenvalues
and signless Laplacian eigenvalues of graphs Kinkar Ch. Das*, Sungkyunkwan University, kinkar@mailcity.com
Abstract: Let G=(V,E) be a simple graph. Denote
by D(G) the diagonal matrix of its vertex degrees and by A(G) its adjacency
matrix. Then the Laplacian matrix of G is L(G)=D(G)A(G) and the signless
Laplacian matrix of G is Q(G)=D(G)+A(G). Cvetkovic et al. (D. Cvetkovic, P.
Rowlinson, S. K. Simic, Eigenvalue bounds for the signless Laplacian, Publ.
Inst. Math. (Beogr.) (N.S.) 81 (95) (2007) 1127.) have given a series of 30
conjectures on Laplacian eigenvalues and signless Laplacian eigenvalues of G
(see also, M. Aouchiche, P. Hansen, A survey of automated conjectures in
spectral graph theory, Linear Algebra Appl., in press). In this paper we prove
some of them.
Abstract Number : SSA8929202047
 10:30 a.m.
A generalization of Temperley's treenumber
formula and applications in networks Woong Kook
*, University of Rhode Island, andrewk@math.uri.edu Seung Kyoon Shin,
University of Rhode Island
Abstract: In 1964, Temperley proved a formula for
the treenumber $k(G)$ of a finite graph $G$ with $n$ vertices:
$n^{2}k(G)=\det(L(G)+J)$, where $L(G)$ is the Laplacian matrix of $G$ and $J$ is
the matrix each of whose entries is +1. In this paper we will prove a
generalization of this formula: $um=\det(M+U)$, where $M$ is a matrix such that
the sum of the entries in each row and each column is zero, $U$ a rank 1 matrix,
$m$ the value of any cofactor of $M$, and $u$ the sum of all entries in $U$. As
an application of this generalization, we give a simple and elegant
combinatorial interpretation of the amount of information contained in all
possible paths between a pair of nodes in a weighted network $G$ which
Stephenson and Zelen calculated in 1989 by inverting the matrix $L(G)+J$.
Abstract Number : SSA8929080419
 Saturday, December 19, 2009, 2:30 p.m  5:50 p.m.
Special Session on Combinatorial Matrix Theory (Code: SS8A)
Room [TBA], Ehwa Women University Organizers of this session: SukGeun
Hwang, Kyungpook National University sghwang@knu.ac.kr Bryan Shader, University of Wyoming, bshader@uwyo.edu Chair: Richard A. Brualdi, University of Wisconsin, brualdi@math.wisc.edu
 2:30 p.m.
Minum rank and skewsymmetric matrices Bryan Shader*,
University of Wyoming, bshader@uwyo.edu
Abstract: TBA (KMS submission)
Abstract Number : NONE
 3:00 p.m.
An algebraic structure of Riordan matrices GiSang Cheon*, Sungkyunkwan University, gscheon@skku.edu SungTae Jin, Sungkyunkwan
University
Abstract: We
consider an infinite lower triangular matrix
$L=[\ell_{n,k}]_{n,k\in\mathrm{\mathbf{N_{0}}}}$ and a sequence
$\Omega=(\o_n)_{n\in\mathrm{\mathbf{N_{0}}}}$ such that every element
$\ell_{n+1,k+1}$ except column 0 can be expressed as a linear combination with
coefficients in $\Omega$ of the elements lying on the slanting line $axby=0$
starting from $\ell_{n,k}$ i.e., $$
\ell_{n+1,k+1}=\o_{0}\ell_{n,k}+\o_{1}\ell_{na,k+b}+\o_{2}\ell_{n2a,k+2b}+\cdots$$
where $a$ and $b$ are integers with $a+b>0$ and $b\ge0$. This concept
generalizes the $A$sequence of Riordan matrices. As a result, we explore new
sequences of a Riordan matrix.
Abstract Number : SSA8930092140
 3:30 p.m.
Hadamard Equivalence on Binary Matrices  New
Combinatoral Problem HongYeop Song*, Yonsei
University, hysong@yonsei.ac.kr
Abstract: TBA (KMS submission)
Abstract Number : SSA81019191214
 4:00 p.m.
Perfect Matchings in Clawfree Cubic
Graphs Sangil Oum*, KAIST, sangil@kaist.edu
Abstract: TBA (KMS submission)
Abstract Number :
SSA81019191016
 4:30 p.m.
The hitting time subgroup, {\L }ukasiewicz paths
and Faber polynomials Hana Kim*, Sungkyunkwan
University, hakkai14@skku.edu GiSang Cheon,
Sungkyunkwan University, Louis W. Shapiro, Howard
University
Abstract: A \L
ukasiewicz path (or more briefly Lpath) of length $n$ is a lattice path
starting at the origin and ending at $(n,0)$ whose steps are of the type
$(1,j)$, $j=1,0,1,2,\ldots$ and these paths cannot go below the $x$axis. It
is known that the number of all {\L }ukasiewicz paths of length $n$ is the
$n$th Catalan number. The concept of Lpaths connects several disparate
subjects, the hitting time subgroup of the Riordan group, restricted and
unrestricted lattice paths, and the Faber polynomials from complex variables.
These connections are the main topic of this talk.
Abstract Number :
SSA8930103140
 4:55 p.m.
Comparing Zagreb indices for connected
graphs Batmend Horoldagva*, Sungkyunkwan
University, b_khorlo@yahoo.com
Abstract: TBA (KMS submission)
Abstract Number :
SSA81019191349

5:20 p.m. Fibonacci sequences and the winning conditions
for the blackout game SangGu Lee*,
Sungkyunkwan University, sglee@skku.edu Duksun
Kim, Sungkyunkwan University, Faqir M. Bhatti, Lahore Univ of Management
Sciences
Abstract: The
blackout game(Lightout Game, Merlin Game, $\sigma$+Game) is a popular game on a
squareboard. When we toggle a button with black or white color, it changes the
color of itself and other buttons which have common edges. It is similar to the
``Reversi(Othello) Game". With this rule, we can win the game when we have a
squareboard with all same colors after some clicks. Here we show that the
winning conditions for the general $m \times n$ blackout games are related with
the determinant of a block triangular matrix generated by a given blackout game.
The Fibonacci sequences are used to get the determinant of the block triangular
matrix. We investigate some properties of a generalized Fibonacci sequences with
a winnable condition for the blackout game. Also, we introduce a JAVA simulation
tool that gives us winnable conditions for an arbitrary given $m \times n$
blackout game.
Abstract Number : SSA8831100743
* If we have one more talk, we may add at 5:45 p.m.

