• Communications of the Korean Mathematical Society
• /
• v.39 no.3
• /
• pp.803-819
• /
• 2024

In our study, the integration of fuzzy graphs into classical graph theory gives rise to a novel concept known as "Fuzzy Super Subdivision." Let SS_f (G) be the fuzzy super subdivision graphs, by substituting a complete bipartite graph k_(2,m) (m = 1, 2, . . .) for each edge of a fuzzy graph. The attributes and properties of this newly proposed concept are briefly outlined, in addition to illustrative examples. Furthermore, significant findings are discussed on connectivity, size, degree and order of fuzzy super subdivision structures. To illustrate the practical implications of our approach, we present an application focused on analyzing the growth of infections in blood or urine samples using the Fuzzy Super Subdivision model.

• Honam Mathematical Journal
• /
• v.38 no.1
• /
• pp.71-84
• /
• 2016

The aim of this work is to compute the volume of the graph polytope associated with various type of finite simple graphs composed of paths and stars. Recurrence relations are obtained using the recursive volume formula (RVF) which was introduced in Lee and Ju ([3]). We also discussed the relationship between the volume of the graph polytopes and the number of linear extensions of the associated posets for given bipartite graphs.

• Proceedings of the Korean Institute of Industrial Safety Conference
• /
• 2004.04a
• /
• pp.366-371
• /
• 2004

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.6 no.8
• /
• pp.1913-1925
• /
• 2012

In order to efficiently utilize limited radio resources, resource allocation schemes in OFDMA-based wireless networks have gained intensive attention recently. Instead of improving the throughput performance, the utility is adopted as the metric for resource allocation, which provides reasonable methods to build up the relationship between user experience and various quality-of-service (QoS) metrics. After formulating the optimization problem by using a weighted bipartite graph, a modified bipartite matching method is proposed to find a suboptimal solution for the resource allocation problem in OFDMA-based wireless systems with feasible computational complexity. Finally, simulation results are presented to validate the effectiveness of the proposed method.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.23 no.4
• /
• pp.1-10
• /
• 1998

We consider the precedence-constrained knapsack problem. which is a knapsack problem with precedence constraints imposed on the set of variables. Especially, we focus on the case where the precedence constraints cir be represented as a bipartite graph, which occurs most frequently in applications. Based on the previous studios for the general case, we specialize the polyhedral results on the related polytope and derive stronger results on the facet-defining properties of the inequalities.

• Kyungpook Mathematical Journal
• /
• v.56 no.3
• /
• pp.647-655
• /
• 2016

Let H be a graph, and $k{\geq}{\chi}(H)$ an integer. We say that H has a cyclic Gray code of k-colourings if and only if it is possible to list all its k-colourings in such a way that consecutive colourings, including the last and the first, agree on all vertices of H except one. The Gray code number of H is the least integer $k_0(H)$ such that H has a cyclic Gray code of its k-colourings for all $k{\geq}k_0(H)$. For complete bipartite graphs, we prove that $k_0(K_{\ell},r)=3$ when both ${\ell}$ and r are odd, and $k_0(K_{\ell},r)=4$ otherwise.

• Journal of Korea Spatial Information System Society
• /
• v.11 no.2
• /
• pp.13-18
• /
• 2009

This paper presents the implementation procedure of encoding and decoding algorithms for Tornado code that can provide fault tolerance for storage and transmission system. The degree distribution satisfying heavy tail distribution is produced. Based on this distribution, a good random irregular bipartite graph is attained after plenty of trails. Such graph construction is proved to be efficient, and the experiments also demonstrate that the implementation obtains good performance in terms of decoding overhead.

• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
• /
• 2010.04a
• /
• pp.11-13
• /
• 2010

Combined with the indeterminate boundaries of spatial objects, n:m correspondences makes an object-based matching be a complex problem. In this study, we model the boundary of a polygon object with fuzzy model and describe their overlapping relations as a weighted bipartite graph. Then corresponding pairs including 1:0, 1:1, 1:n and n:m relations are identified using a spectral singular value decomposition.

• Journal of the Chungcheong Mathematical Society
• /
• v.13 no.2
• /
• pp.81-86
• /
• 2001

In this paper, we present the proof of the property for interior metric space and geodesic space.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.1
• /
• pp.331-342
• /
• 2017

Let R be a commutative ring with nonzero identity and G be a nontrivial finite group. Also, let Z(R) be the set of zero-divisors of R and, for $a{\in}Z(R)$, let $ann(a)=\{r{\in}R{\mid}ra=0\}$. The annihilator graph of the group ring RG is defined as the graph AG(RG), whose vertex set consists of the set of nonzero zero-divisors, and two distinct vertices x and y are adjacent if and only if $ann(xy){\neq}ann(x){\cup}ann(y)$. In this paper, we study the annihilator graph associated to a group ring RG.