• Communications of the Korean Mathematical Society
• /
• v.32 no.4
• /
• pp.805-810
• /
• 2017

Let $C_n$ be the cycle graph of order n on the vertices $v_0,v_1,{\ldots},v_n$ and $C^k_n$ be the k-th power of $C_n$. In this article we determine the hull-number of $C^k_n$.

• Journal of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.437-454
• /
• 2000

Let C be a smooth k-gonal curve of genus g. We study the number of pencils of degree k on C. In case $g\geqk(k-a)/2$ we state a conjecture based on a discussion on plane models for C. From previous work it is known that if C possesses a large number of pencils then C has a special plane model. From this observation the conjectures are split up in two cases : the existence of some types of plane curves should imply the existence of curves C with a given number of pencils; the non-existence of plane curves should imply the non-existence of curves C with some given large number of pencils. The non-existence part only occurs in the range $k(k-1)/2\leqg\leqk(k-1)/2] if k\geq7$. In this range we prove the existence part of the conjecture and we also prove some non-existence statements. Those result imply the conjecture in that range for $k\leq10$. The cases $k\leq6$ are handled separately.

• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.1
• /
• pp.245-250
• /
• 2020

Let γt(G) and τ(G) denote the total domination number and vertex cover number of graph G, respectively. In this paper, we study the total domination number of the central tree C(T) for a tree T. First, a relationship between the total domination number of C(T) and the vertex cover number of tree T is discussed. We characterize the central trees with equal total domination number and independence number. Applying the first result, we improve the upper bound on the total domination number of C(T) and solve one open problem posed by Kazemnejad et al..

• Journal of the Korean Mathematical Society
• /
• v.44 no.6
• /
• pp.1213-1231
• /
• 2007

The domination number ${\gamma}(G)$ of a graph G=(V,E) is the minimum cardinality of a subset of V such that every vertex is either in the set or is adjacent to some vertex in the set. The bondage number of b(G) of a graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number greater than ${\gamma}(G)$. In this paper, we calculate the bondage number of the Cartesian product of cycles $C_3\;and\;C_n$ for all n.

• Annals of Fuzzy Mathematics and Informatics
• /
• v.16 no.3
• /
• pp.301-316
• /
• 2018

In this paper, the concept of connected geodesic number, $gn_c(G)$, of a fuzzy graph G is introduced and its limiting bounds are identified. It is proved that all extreme nodes of G and all cut-nodes of the underlying crisp graph $G^*$ belong to every connected geodesic cover of G. The connected geodesic number of complete fuzzy graphs, fuzzy cycles, fuzzy trees and of complete bipartite fuzzy graphs are obtained. It is proved that for any pair k, n of integers with $3{\leq}k{\leq}n$, there exists a connected fuzzy graph G : (V, ${\sigma}$, ${\mu}$) on n nodes such that $gn_c(G)=k$. Also, for any positive integers $2{\leq}a<b{\leq}c$, it is proved that there exists a connected fuzzy graph G : (V, ${\sigma}$, ${\mu}$) such that the geodesic number gn(G) = a and the connected geodesic number $gn_c(G)=b$.

• Biomedical Science Letters
• /
• v.11 no.3
• /
• pp.259-266
• /
• 2005

Mast cells and goblet cells have been known to protect the host against parasites. In this study, we examined the response of the mast cells and goblet cells over a period of 6 weeks in the duodenum, jejunum and ileum of C3H/HeN and C57BL/6 mice infected with Echinostoma hortense (E. hortense). In addition, we investigated whether the worm recovery rate of uninfected mice (the control group) or E. hortense-infected mice (the experimental group) was associated with the number of mast cells and goblet cells. The worm recovery rate was higher in the C3H/HeN mice than in the C57BL/6 mice. The number of goblet cells significantly increased in the experimental group of the C3H/HeN and C57BL/6 mice compared with the control group of both strains (P<0.005). Worm recovery peaked 3 weeks after the infection of the C57BL/6 mice and at 2 weeks after the infection of the C3H/HeN mice, and it was higher in the duodenum than in the jejunum and ileum. However, the infected site in the intestine had no relation with worm expulsion. In the C3H/HeN and C57BL/6 mice, the number of goblet cells in the experimental group was significantly higher than that in the control group (P<0.005). The number reached a peak 2 weeks after the infection and it even increased in duodenum, jejunum and ileum. The increased number of goblet cells was retained 6 weeks after infection. The number of goblet cells was higher in the C3H/HeN mice than in the C57BL/6 mice (P<0.01). These results indicate that goblet cells are related with the worm expulsion. Furthermore, immunohistostaining of the antral intestinal walls for lectin showed the significant increase of the number of goblet cells in the experimental group (P<0.001). The high infection rate in the duodenum was found during the early infection. An increased infection rate in the jejunum and ileum was found 3 weeks after infection and the infection rate was higher in the C3H/HeN mice than in the C57BL/6 mice. Taken together, the present study indicates that goblet cells, rather than mast cells, may play critical roles in parasite expulsion.

• Communications of the Korean Mathematical Society
• /
• v.19 no.1
• /
• pp.159-167
• /
• 2004

In [1], a relative root Nielsen number $N_{rel}(f;\;c)$ is introduced which is a homotopy invariant lower bound for the number of roots at $c\;{\in}\;Y$ for a map of pairs of spaces $f\;:\;(X,\;A)\;{\rightarrow}\;(Y,\;B)$. In this paper, we obtain a minimum theorem for $N_{rel}(f;\;c)$ under some new assumptions on the spaces and maps which are different from those in [1].

• ETRI Journal
• /
• v.42 no.4
• /
• pp.518-526
• /
• 2020

This paper presents an efficient hardware random-number generator based on a beta source. The proposed generator counts the values of "0" and "1" and provides a method to distinguish between pseudo-random and true random numbers by comparing them using simple cumulative operations. The random-number generator produces labeled data indicating whether the count value is a pseudo- or true random number according to its bit value based on the generated labeling data. The proposed method is verified using a system based on Verilog RTL coding and LabVIEW for hardware implementation. The generated random numbers were tested according to the NIST SP 800-22 and SP 800-90B standards, and they satisfied the test items specified in the standard. Furthermore, the hardware is efficient and can be used for security, artificial intelligence, and Internet of Things applications in real time.

• Communications of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.695-704
• /
• 2018

In this paper, firstly we compute the spectral norm of g-circulant matrices $C_{n,g}=g-Circ(c_0,c_1,{\cdots},c{_{n-1}})$, where $c_i{\geq}0$ or $c_i{\leq}0$ (equivalently $c_i{\cdot}c_j{\geq}0$). After, we compute the spectral norms, determinants and inverses of the g-circulant matrices with the Fibonacci and Lucas numbers.