• 대한원격탐사학회지
• /
• 제20권1호
• /
• pp.57-64
• /
• 2004

In GIS-based network analysis, topological measure of network structure can be considered as one of important factors in the urban transportation analysis. Related to this measure, it is known that the connectivity indices such as alpha index and gamma index, which mean degree of network connectivity and complexity on a graph or a circuit, provide fundamental information. On the other hand, shimbel index is one of GIS-based spatial metrics to characterize degree of network concentration. However, the approach using these quantitative indices has not been widely used in practical level yet. In this study, an application program, in complied as extension, running on ArcView- GIS is implemented and demonstrated case examples using basic layers such as road centerline and administrative boundary. In this approach, geo-spatial imagery can be effectively used to actual applications to determine the analysis zone, which is composed of networks to extract these indices. As the results of the implementation and the case examples, it is notified that alpha and gamma indices as well as shimbel index can be used as referential data or auxiliary information for urban planning and transportation planning.

• Journal of applied mathematics & informatics
• /
• 제36권3_4호
• /
• pp.307-315
• /
• 2018

Let G be a simple connected graph with n vertices and m edges, with a sequence of vertex degrees $d_1{\geq}d_2{\geq}{\cdots}{\geq}d_n$ > 0. A vertex-degree topological index, referred to as harmonic index, is defined as $H={\sum{_{i{\sim}j}}{\frac{2}{d_i+d_j}}$, where i ~ j denotes the adjacency of vertices i and j. Lower and upper bounds of the index H are obtained.

• Journal of applied mathematics & informatics
• /
• 제34권5_6호
• /
• pp.479-486
• /
• 2016

In this paper we define the edge version of harmonic index and harmonic polynomial of a graph G. We computed explicit formulas for the edge version of harmonic index and harmonic polynomial of many well known classes of graphs.

• Journal of applied mathematics & informatics
• /
• 제29권5_6호
• /
• pp.1075-1080
• /
• 2011

Among the numerous topological indices considered in chemical graph theory, only a few have been found noteworthy in practical application, Randi$\acute{c}$ index is one of them. The dendrimer nanostars is a synthesized molecule built up from branched unit called monomers. In this article, we compute the Randi$\acute{c}$ index of two types of polymer dendrimers and a fullerene dendrimer.

• Journal of applied mathematics & informatics
• /
• 제29권1_2호
• /
• pp.327-335
• /
• 2011

Explicit formulas are given for the first and second Zagreb index, degree-distance and Wiener-type invariants of splice and link of graphs. As a consequence, the first and second Zagreb coindex of these classes of composite graphs are also computed.

• Korean Journal of Mathematics
• /
• 제27권3호
• /
• pp.613-627
• /
• 2019

Consider a connected molecular graph G = (V, E) where V is the set of vertices and E is the set of edges. In G, vertices represent the atoms and edges represent the covalent bonds between atoms. In graph G, every edge (say) e = uv will be connected by two atoms u and v. The edge Szeged index is a topological index which has been introduced by Ivan Gutman. In this paper, we have computed edge Szeged indices of a hydrocarbon family called Benzene ring and is denoted by $(BR)_{n{\times}n}$.

• 한국주거학회논문집
• /
• 제22권2호
• /
• pp.101-109
• /
• 2011

Until now, several comparative approaches were developed within the studies of Korean, Chinese, and Japanese traditional housings. In those studies, however, each space in the traditional houses was only treated in individual and fragmentary manners, and they lacked the interpretation of the topological attribute of each space within a holistic structure organized by unit spaces, and of the cultural-behavioral meaning of them within a holistic space-use pattern of the housing. The topological attribute and behavioral meaning can be analyzed and interpreted with the quantitative spatial analysis method such as Space Syntax. This study aims to analyze the traditional housings in Korea, China and Japan in the holistic aspect of spatial structure using Space Syntax, and to compare the analysis results with relating the structural attributes to the space-use pattern. In this study, the 'Banga' in Chosun era, the 'Siheyuan' in Ming-Ching era, and the 'Shoinzukuri' in Edo era were selected as the analysis subjects. The integration indices were calculated from the convex maps representing the subjects, and the common and different attributes of the three subjects were defined through comparative analyses.

• Environmental Analysis Health and Toxicology
• /
• 제14권1_2호
• /
• pp.65-73
• /
• 1999

Dioxins refer to a family of chemicals comprising 75 polychlorinated dibenzo-p-dioxin (PCDD) and 135 polychlorinated dibenzo-p-furan (PCDF) congeners, which may cause skin disorder, human immune system disruption, birth defects, severe hormonal imbalance, and cancer. The effects of exposure of dioxin-like compounds such as PCBs are mediated by binding to the aryl hydrocarbon receptor (AHR), which is a ligand-activated transcription factor. To grasp physicochemical factors affecting human toxicity of dioxins, six geometrical and topological indices, eleven thermodynamic variables, and quantum mechanical descriptors including ESP (electrostatic potential) were analyzed using QSAR and semi-empirical AM1 method. Planar dioxins with high lipophilicity and large surface tension show the probability that negative electrostatic potential in the lateral oxygen may make hydrogen bonding with DNA bases to be a carcinogen.

• Journal of applied mathematics & informatics
• /
• 제31권5_6호
• /
• pp.595-608
• /
• 2013

Let G = (V, E) be a simple connected graph. The sets of vertices and edges of G are denoted by V = V (G) and E = E(G), respectively. In such a simple molecular graph, vertices represent atoms and edges represent bonds. The distance between the vertices $u$ and $v$ in V (G) of graph G is the number of edges in a shortest path connecting them, we denote by $d(u,v)$. In graph theory, we have many invariant polynomials for a graph G. In this paper, we focus on the Schultz polynomial, Modified Schultz polynomial, Hosoya polynomial and their topological indices of a molecular graph circumcoronene series of benzenoid $H_k$ and specially third member from this family. $H_3$ is a basic member from the circumcoronene series of benzenoid and its conclusions are base calculations for the Schultz polynomial and Hosoya polynomial of the circumcoronene series of benzenoid $H_k$ ($k{\geq}3$).

• Journal of applied mathematics & informatics
• /
• 제38권1_2호
• /
• pp.189-200
• /
• 2020

Let G be a simple connected graph with n vertices and m edges. Denote by d₁ ≥ d₂ ≥ ⋯ ≥ d_n > 0 and d(e₁) ≥ d(e₂) ≥ ⋯ ≥ d(e_m) sequences of vertex and edge degrees, respectively. If vertices v_i and v_j are adjacent, we write i ~ j. The general sum-connectivity index is defined as 𝒳_α(G) = ∑_i~j(d_i + d_j)^α, where α is an arbitrary real number. Firstly, we determine a relation between 𝒳_α(G) and 𝒳_α-1(G). Then we use it to obtain some new bounds for 𝒳_α(G).