• The Journal of Natural Sciences
• /
• v.12 no.1
• /
• pp.1-9
• /
• 2002

Let G be a connected graph on n vertices. The pebbling number of graph G, f(G), is the least m such that, however m pebbles are placed on the vertices of G, we can move a pebble to any vertex by a sequence of moves, each move taking two pebbles off one vertex and placing one on an adjacent vertex. In this paper, we compute the pebbling number of the Petersen Graph. We also show that the pebbling number of the categorical Product G.H is (m+n)h where G is the complete bipartite graph $K_{m,n}$ and H is the complete graph with $h(\geq4)$ vertices.

• Journal of applied mathematics & informatics
• /
• v.42 no.3
• /
• pp.511-520
• /
• 2024

In this paper, we introduce the concept of split and non-split tree (D, C)- set of a connected graph G and its associated color variable, namely split tree (D, C) number and non-split tree (D, C) number of G. A subset S ⊆ V of vertices in G is said to be a split tree (D, C) set of G if S is a tree (D, C) set and ⟨V - S⟩ is disconnected. The minimum size of the split tree (D, C) set of G is the split tree (D, C) number of G, γ_χST (G) = min{|S| : S is a split tree (D, C) set}. A subset S ⊆ V of vertices of G is said to be a non-split tree (D, C) set of G if S is a tree (D, C) set and ⟨V - S⟩ is connected and non-split tree (D, C) number of G is γ_χST (G) = min{|S| : S is a non-split tree (D, C) set of G}. The split and non-split tree (D, C) number of some standard graphs and its compliments are identified.

• Proceedings of the Korean Society for Quality Management Conference
• /
• 1998.11a
• /
• pp.295-300
• /
• 1998

Recently graphical modelling is being studied as a useful process analysis tool for exploratory causal analysis. Graphical modelling is a presentation method that uses graphs to describe statistical models of the structures of multivariate data. This paper describes an application of this graphical modeling with two cases from the automotive parts industry. One case is the unbalance problem of the pulley, an automotive generator part. There is multivariate data of the product from each of the processes which are connected in the series. By means of exploratory causal analysis between the variables using graphical modeling, the key processes which causes the variation of the final characteristics and their mechanism of the causal relationship have become clear. Another case is, also, the unbalanced problem of automotive starter parts which consists of many parts and is manufactured by complex machinery and assembling process. By means of the similar technique, the key processes are obtained easily and the results are reasonable from technical knowledge.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.2
• /
• pp.353-363
• /
• 2011

Let k $\geq$ 1 be an integer, and let G be a 2-connected graph of order n with n $\geq$ max{7, 4k+1}, and the minimum degree $\delta(G)$ $\geq$ k+1. In this paper, it is proved that G has a fractional k-factor excluding any given edge if G satisfies max{$d_G(x)$, $d_G(y)$} $\geq$ $\frac{n}{2}$ for each pair of nonadjacent vertices x, y of G. Furthermore, it is showed that the result in this paper is best possible in some sense.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.6
• /
• pp.1691-1701
• /
• 2018

New inclusion sets are obtained for the eigenvalues of real matrices for which the all 1's vector is an eigenvector, i.e., the constant row-sum real matrices. A number of examples are provided. This paper builds upon the work of the authors in [7]. The results of this paper are in terms of $Ger{\check{s}}gorin$ discs of the second type. An application of the main theorem to bounding the algebraic connectivity of connected simple graphs is obtained.

• Communications of the Korean Mathematical Society
• /
• v.24 no.2
• /
• pp.161-169
• /
• 2009

In this paper, we introduce the generalized ideal-based zero-divisor graph structure of near-ring N, denoted by $\widehat{{\Gamma}_I(N)}$. It is shown that if I is a completely reflexive ideal of N, then every two vertices in $\widehat{{\Gamma}_I(N)}$ are connected by a path of length at most 3, and if $\widehat{{\Gamma}_I(N)}$ contains a cycle, then the core K of $\widehat{{\Gamma}_I(N)}$ is a union of triangles and rectangles. We have shown that if $\widehat{{\Gamma}_I(N)}$ is a bipartite graph for a completely semiprime ideal I of N, then N has two prime ideals whose intersection is I.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2011.05a
• /
• pp.43-46
• /
• 2011

A novel circuit structure of dual-band bandstop filters is proposed in this paper. This structure comprises two shunt-connected tri-section stepped impedance resonators with a transmission line in between. Theoretical analysis from the equivalent circuit and design procedures are described. We represented graphs for filter design from the derived synthesis equations by resonance condition of circuits. Notably, advantages of the proposed filter structure are compact size in design, wide range of realizable resonance frequency ratio, and more realizable impedances.

• Journal of Institute of Control, Robotics and Systems
• /
• v.18 no.3
• /
• pp.218-223
• /
• 2012

Maintenance and improvement of the graph connectivity is very important for decentralized multi-agent systems. Although the CBBA (Consensus-Based Bundle Algorithm) guarantees suboptimal performance and bounded convergence time, it is only valid for connected graphs. In this study, we apply a decentralized estimation procedure that allows each agent to track the algebraic connectivity of a time-varying graph. Based on this estimation, we design a decentralized gradient controller to maintain the graph connectivity while agents are traveling to perform assigned tasks. Simulation result for fully-actuated first-order agents that move in a 2-D plane are presented.

• Proceedings of the Korea Society for Simulation Conference
• /
• 2005.05a
• /
• pp.89-92
• /
• 2005

Each 3D visualization program has its own different structure as for the purpose. This paper describes the design and development of an on-line 3D core data visualization program, $RocDis^{TM}$, for the nuclear simulator. It is possible to analyze the inside of the core status including neutron flux, relative power, moderator and fuel temperature in 3D distribution. Some of other essential information, axial flux distribution etc. could also display in 2D graphs. This program would be design, tuning and training for the simulator core model.

• The Journal of the Korea institute of electronic communication sciences
• /
• v.5 no.3
• /
• pp.239-244
• /
• 2010

In this paper, we study the adjacency matrix of a minimal connected quadrangular graph G, and then we obtain an upper bound on |E(G)| for such a graph G, and we obtain the graph for which the upper bound is attained. In addition, we obtain an upper bound on |E(G)| for a critical matching covered quadrangular graph G.