• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.89-100
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• 2015

In this paper, we present exact formulae for the multiplicatively weighted Harary indices of join, tensor product and strong product of graphs in terms of other graph invariants including the Harary index, Zagreb indices and Zagreb coindices. Finally, We apply our result to compute the multiplicatively weighted Harary indices of fan graph, wheel graph and closed fence graph.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.615-631
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• 2023

A power cordial labeling of a graph G = (V (G), E(G)) is a bijection f : V (G) → {1, 2, ..., |V (G)|} such that an edge e = uv is assigned the label 1 if f(u) = (f(v))ⁿ or f(v) = (f(u))ⁿ, For some n ∈ ℕ ∪ {0} and the label 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. In this paper, we investigate power cordial labeling for helm graph, flower graph, gear graph, fan graph and jewel graph as well as larger graphs obtained from star and bistar using graph operations.

• Journal of Applied and Pure Mathematics
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• v.4 no.5_6
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• pp.317-329
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• 2022

In this paper we investigate the pair difference cordial labeling behaviour of m- copies of K₄, subdivision of star, fan, comb graphs.

• Communications of the Korean Institute of Information Scientists and Engineers
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• v.5 no.1
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• pp.42-49
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• 1987

This paper describes test-pattern generation and it;s sequence for fan out-free Combinational logic network with multiple faults. The method for detecting multiple faults, in systematic way, is established by using characteristic graphs. This method is applied even in the case of fan out-reconvergent combinational logic networks. In this case, the network is decomposed into a set of fan out-free sybnetworks so as to use the characteristic graphs, and minimal test patterns are generated seperately. The each test set is combined and the test pattern for fan out-reconvergent networks are derived. According to corresponding characteristic graph, additional test patterns to detect multiple faults are simply derived.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.497-506
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• 2021

Let G be a graph. Let f : V (G) → {0, 1, …, k - 1} be a function where k ∈ ℕ and k > 1. For each edge uv, assign the label $f(uv)={\lceil}{\frac{f(u)+f(v)}{2}}{\rceil}$. f is called k-total mean cordial labeling of G if ${\mid}t_{mf}(i)-t_{mf}(j){\mid}{\leq}1$, for all i, j ∈ {0, 1, …, k - 1}, where t_mf (x) denotes the total number of vertices and edges labelled with x, x ∈ {0, 1, …, k-1}. A graph with admit a k-total mean cordial labeling is called k-total mean cordial graph.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.37 no.3
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• pp.267-273
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• 2013

In order to provide effective operating conditions for the fan in a wet cooling tower with film fill, a new program to search for the minimum fan power was developed using a model of the optimal total annual cost of the tower based on Merkel's model. In addition, a type of design map for a cooling tower was also developed. The inlet water temperature and heat load were considered as key parameters. The present program was first validated using several typical examples. The results showed that for a given heat load, a three-dimensional graph of the fan power (z-axis), mass flux of air (x-axis, minimum fan power), and inlet water temperature (y-axis, maximum of minimum fan power) showed a saddle configuration. The minimum fan power increased as the heat load increased. The conventionally known fact that the most effective cooling tower operation coincides with a high inlet water temperature and low air flow rate can be replaced by the statement that there exists an optimum mass flux of air corresponding to a minimum fan power for a given inlet water temperature, regardless of the heat load.

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.221-238
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• 2020

Let G = (V (G), E(G)) be a graph and let g : V (G) → S₃ be a function. For each edge xy assign the label r where r is the remainder when o(g(x)) is divided by o(g(y)) or o(g(y)) is divided by o(g(x)) according as o(g(x)) ≥ o(g(y)) or o(g(y)) ≥ o(g(x)). The function g is called a group S₃ cordial remainder labeling of G if |v_g(i)-v_g(j)| ≤ 1 and |e_g(1)-e_g(0)| ≤ 1, where v_g(j) denotes the number of vertices labeled with j and e_g(i) denotes the number of edges labeled with i (i = 0, 1). A graph G which admits a group S₃ cordial remainder labeling is called a group S₃ cordial remainder graph. In this paper, we prove that subdivision of graphs admit a group S₃ cordial remainder labeling.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.643-651
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• 2005

In the first part of this paper we investigate several statements concerning infinite maximal planar graphs which are equivalent in finite case. In the second one, for a given induced $\theta$-path (a finite induced path whose endvertices are adjacent to a vertex of infinite degree) in a 4-connected VAP-free maximal planar graph containing a vertex of infinite degree, a new $\theta$-path is constructed such that the resulting fan is tight.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.11
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• pp.4347-4366
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• 2015

Distinguished with traditional strategies which offload an application's computation to a single server, parallel computation offloading can promote the performance by simultaneously delivering the computation to multiple computing resources around the mobile terminal. However, due to the variability of communication and computation environments, static application component multi-partitioning algorithms are difficult to maintain the optimality of their solutions in time-varying scenarios, whereas, over-frequent algorithm executions triggered by changes of environments may bring excessive algorithm costs. To this end, an adaptive application component mapping algorithm for parallel computation offloading in variable environments is proposed in this paper, which aims at minimizing computation costs and inter-resource communication costs. It can provide the terminal a suitable solution for the current environment with a low incremental algorithm cost. We represent the application component multi-partitioning problem as a graph mapping model, then convert it into a pathfinding problem. A genetic algorithm enhanced by an elite-based immigrants mechanism is designed to obtain the solution adaptively, which can dynamically adjust the precision of the solution and boost the searching speed as transmission and processing speeds change. Simulation results demonstrate that our algorithm can promote the performance efficiently, and it is superior to the traditional approaches under variable environments to a large extent.

• The Journal of Korean Society for Radiation Therapy
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• v.25 no.2
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• pp.175-180
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• 2013

Purpose: Modern radiation therapy technique such as IGRT has become a routine clinical practice on LINAC for decrease patient's set-up error. CBCT can be used to adjust patient set-up error and treat patient more accurately. The Purpose of this study is to evaluate field size of CBCT for improving Image quality and suggest reference date of CBCT field size. Materials and Methods: Image date were acquired using KV CBCT and Catphan phantom (Half fan and full fan mode were scanned from 2 ~16 cm, at intervals of 2 cm). Field size were categorized by Small field size (2 cm, 4 cm), Medium field size (8 cm, 10 cm), Large field size (more than 14 cm) and evaluate. To estimated the CTDi using CTDi phantom and Ion chamber. Results: CT number linearity of Small and Large field size are greater than Medium field size. Spatial resolution are not significantly different without Small field size. But half fan mode is more different than full fan mode. In full fan, except Medium field size, all field size exceed recommendation for HU uniformity. But half pan has stability for all field except Small field size. CTDi makes radical sign function graph in Medium field size. Conclusion: The worst result was given by Small field size for Image quality and practically. Medium field size can be useful to prevent patient from radiation exposure and give better Image quality. So this study recommends that Medium field size (8~10 cm) is more suitable for CBCT.