• Journal of applied mathematics & informatics
• /
• v.42 no.3
• /
• pp.663-680
• /
• 2024

The zero divisor graph is the most basic way of representing an algebraic structure as a graph. For any commutative ring R, each element is a vertex on the zero divisor graph and two vertices are defined as adjacent if and only if the product of those vertices equals zero. In this research, we determine some topological indices such as the Wiener index, the edge-Wiener index, the hyper-Wiener index, the Harary index, the first Zagreb index, the second Zagreb index, and the Gutman index of zero divisor graph of integers modulo prime power and its direct product.

• Journal of applied mathematics & informatics
• /
• v.31 no.3_4
• /
• pp.533-544
• /
• 2013

The multiplicative version of Wiener index (${\pi}$-index), proposed by Gutman et al. in 2000, is equal to the product of the distances between all pairs of vertices of a (molecular) graph G. In this paper, we first present some sharp bounds in terms of the order and other graph parameters including the diameter, degree sequence, Zagreb indices, Zagreb coindices, eccentric connectivity index and Merrifield-Simmons index for ${\pi}$-index of general connected graphs and trees, as well as a Nordhaus-Gaddum-type bound for ${\pi}$-index of connected triangle-free graphs. Then we study the behavior of ${\pi}$-index upon the case when removing a vertex or an edge from the underlying graph. Finally, we investigate the extremal properties of ${\pi}$-index within the set of trees and unicyclic graphs.

• Journal of applied mathematics & informatics
• /
• v.30 no.3_4
• /
• pp.353-364
• /
• 2012

The Wiener polarity index$W_p(G)$ of a graph G of order $n$ is the number of unordered pairs of vertices $u$ and $v$ of G such that the distance $d_G(u,v)$ between $u$ and $v$ is 3. In this paper the Wiener polarity index of some graph operations are computed. As an application of our results, the Wiener polarity index of a polybuckyball fullerene and $C_4$ nanotubes and nanotori are computed.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.35 no.5A
• /
• pp.466-473
• /
• 2010

Several protocols which are based on tree topology to guarantee the important metrics such as energy efficiency in sensor networks have been proposed. However, studies on the effect of topologies in sensor networks, where base node has a high mobility, are very few. In this paper, we propose a minimum Wiener index tree as a suitable topology to the wireless sensor networks with high mobile base node. The minimum Wiener index spanning tree problem which aims to find a tree with minimum Wiener index from a given weighted graph was proved to be NP-hard. We designed a branch and bound algorithm for this problem. To evaluate the performance of proposed tree, the comparisons with minimum spanning tree in terms of transmission distance, energy consumption during one round, and network lifetime was performed by simulations. Our proposed tree outperformed in transmission distance and energy efficiency but underperformed in lifetime.

• Journal of the Korean Mathematical Society
• /
• v.37 no.4
• /
• pp.545-563
• /
• 2000

An integral transform with the Bessel function Jv(z) in the kernel is considered. The transform is relatd to a singular Sturm-Liouville problem on a half line. This relation yields a Plancherel's theorem for the transform. A Paley-Wiener-type theorem for the transform is also derived.

• The Transactions of the Korean Institute of Electrical Engineers D
• /
• v.49 no.3
• /
• pp.102-110
• /
• 2000

In this paper, Wiener-Hopf design of the two-degree-of-freedom(2DOF) controller configuration is treated for the standard plant model. It is shown that the 2DOF structure makes it possible to treat the design of feedback properties and reference tracking problem separately. Wiener-Hopf factorization technique is used to obtain the optimal controller which minimizes a given quadratic cost index. The class of all stabilizing controllers that yield finite cost index is also characterized. An illustrative example is given for the step reference tracking problem which can not be treated by the conventional H2 controller formula.

• Journal of applied mathematics & informatics
• /
• v.29 no.1_2
• /
• 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.

• KIPS Transactions on Computer and Communication Systems
• /
• v.2 no.5
• /
• pp.191-198
• /
• 2013

It is required to transmit data through shorter path between sensor and base node for real time intrusion detection in wireless sensor networks (WSN) with a mobile base node. Because minimum Wiener index spanning tree (MWST) based routing approach guarantees lower average hop count than that of minimum spanning tree (MST) based routing method in WSN, it is known that MWST based routing is appropriate for real time intrusion detection. However, the minimum Wiener index spanning tree problem which aims to find a spanning tree which has the minimum Wiener index from a given weighted graph was proved to be a NP-hard. And owing to its high dependency on certain nodes, minimum Wiener index tree based routing method has a shorter network lifetime than that of minimum spanning tree based routing method. In this paper, we propose a multi-objective ant colony optimization algorithm to tackle these problems, so that it can be used to detect intrusion in real time in wireless sensor networks with a mobile base node. And we compare the results of our proposed method with MST based routing and MWST based routing in respect to average hop count, network energy consumption and network lifetime by simulation.

• Journal of the Korean Chemical Society
• /
• v.36 no.4
• /
• pp.485-495
• /
• 1992

The viscosities of organic compounds (alcohols, acetates, alkanes, acids, substituted $NH_2$) in liquid states, gas states and the binary mixtures of n-alkane / 1-chloroalkane were calculated by molecular modeling techniques. The molecular descriptors of molecular modeling technique are Molecular connectivity indices, Wiener indices and ad hoc descriptors, which can encode the information of compound properties about the effect of size, branching, cyclization, unsaturation, heteroatom content, polarizability, and so on. The successful results among method have been Molecular connectivity indices, binary mixtures of n-alkane / 1-chloroalkane, Wiener indices for gas state and ad hoc descriptor for liquid states. Also we obtained the regression equations for viscosities using molecular modeling indices for gas, liquid states and binary mixtures of n-alkane / 1-chloroalkane. The calculated viscosity values for organic compounds are in good agreement with experimental results.

• Journal of Forest and Environmental Science
• /
• v.27 no.1
• /
• pp.17-22
• /
• 2011

Based upon the vegetation data of woody plants by plot sampling method in the natural deciduous forest of Mt. Jeombong, the study was carried out to examine importance value, rank abundance curve, and species abundance curve, and comparatively evaluate seven different species diversity indices for Shannon-Wiener index, Simpson index, McIntosh index, Log series, Margalef index, Berger-Parker index, and species richness, according to topographic positions. The minimal area which meant only few more species were increased was 3.48 ha in total. The dominant species of valley were Carpinus cordata, Acer pseudo-sieboldianum, Quercus mongolica, Acer mono, and Abies holophylla, and the dominant species of mid-slope were Quercus mongolica, Acer pseudo-sieboldianum, Carpinus cordata, Tilia amurensis, and Fraxinus rhynchophylla. Moreover, the dominant species of ridge were Quercus mongolica, Acer pseudo-sieboldianum, Tilia amurensis, Fraxinus rhynchophylla, and Acer mono. According to rank abundance curve and species abundance curve, species evenness was also low. All of Log series, species richness, Margalef, and Shannon-Wiener index discriminated that valley had the highest diversity, and ridge had the lowest diversity; but, Simpson index, McIntosh index, and Berger-Parker index represented that mid-slope had the highest diversity, and ridge had the lowest diversity. Uniquely, in Berger-Parker index, mid-slope was the higher value than total.