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Abstract: Wirelength is an important criterion to validate the quality of an embedding of a graph into a host graph and is used in particular in VLSI (Very-Large-Scale Integration) layout designs. Wiener index plays a significant role in mathematical chemistry, cheminformatics, and elsewhere. In this note these two concepts are related by proving that the Wiener index of a host graph is an upper bound for the wirelength of a given embedding. The wirelength of embedding complete ▫$2^p$▫-partite graphs into Cartesian products of paths and/or cycles as the function of the Wiener index is determined. The result is an asymptotic approximation of the general upper bound.
Keywords: Wiener index, embedding, wirelength, complete 2p-partite graph, Cartesian product of graphs, integer labeling
Published in DKUM: 23.09.2024; Views: 0; Downloads: 0
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Abstract: Effective urban transportation no doubt serves as engine room and catalyst for driving national economic development. Significantly, the purpose of urban transport is to provide both passenger and freight mobility over specific parts of urban areas including cities, and its efficiency is characterized upon transporting effectively and achieving economies of scale. Hence, this study examined intra-city mobility and characterization in Lagos, Nigeria. The data was sourced from both primary and secondary sources. Primary data detailed the use of two sets of questionnaires administered to commuters and motorists. 182 copies of questionnaire were randomly administered to commuters, while 60 units of the questionnaire were purposively and conveniently administered to motorists. Descriptive and inferential techniques were used for data analysis. Major findings revealed obvious variations in socio-economic parameters of intra-city trip makers and factors influencing trip making. It was observed that journey to work, school, shopping cum business constituted the major trips characterizing in Lagos. Findings also revealed that high patronage priority was given to most used and preferred means due to vehicle travel speed, trip purpose, and availability than safety and comfortability of modal choice. Regression analysis result revealed that commuters’ modal choice and patronage is statistically influenced by operational attributes of mode (e.g. transit time, delay duration, safety, vehicle condition and transit fare etc.) at Sig. p=0.000 and F14165 15.667 which is greater than table value at 5% significant level. The study recommended among others the formulation and implementation of effective policy for urban transport activities; standardization of service operations and expansion of infrastructural facilities including the last-mile in the city.
Keywords: urban mobility, transportation, mobility index, Lagos
Published in DKUM: 22.08.2024; Views: 81; Downloads: 6
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Keywords: software maintenance, maintainability measurement, Maintainability Index, software metrics, Java, object-oriented software
Published in DKUM: 20.05.2024; Views: 196; Downloads: 9
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Abstract: Contemporary societies, whether they have reached advanced levels of economic and social development or are still developing, need to prioritise the implementation of circular economy practices. This will facilitate the shift towards regenerative, sustainable, and closed-loop industrial systems. For now, there are some efforts to encourage patterns of production and consumption through changes in economic trends, development of institutional frameworks, harmonising regulations in the field of environmental protection, and raising the level of social awareness to achieve, above all, greater efficiency of resources. Extensive literature that deals with monitoring the implementation of the circular economy already indicates the existence of numerous barriers in this process but also notices some incentives for raising the degree of circularity of the observed systems. In this paper, the question of whether a single value can represent the level of circularity of the chosen material/product chain is researched. An overview of barriers and drivers for implementing circular economy strategies is given to structure a proper metric framework in correlation to the research question. The objective was to simplify the monitoring of circularity by developing a unique index for comparing material/product chains in similar systems. This was accomplished by using the circular material use (CMU) rate introduced in the European Union and modifying it for financial data calculation. As a result, the circular economy index, which covers all 9R strategies (CEIR), is obtained. The practical verification of model applicability was shown by determining the degree of circularity achieved for passenger cars in the four observed EU countries.
Keywords: barriers, 9R framework, circular material use rate, circular economy index, passenger cars
Published in DKUM: 19.03.2024; Views: 296; Downloads: 17
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Abstract: Szeged-like topological indices are well-studied distance-based molecular descriptors, which include, for example, the (edge-)Szeged index, the (edge-)Mostar index, and the (vertex-)PI index. For these indices, the corresponding polynomials were also defined, i.e., the (edge-)Szeged polynomial, the Mostar polynomial, the PI polynomial, etc. It is well known that, by evaluating the first derivative of such a polynomial at x = 1, we obtain the related topological index. The aim of this paper is to introduce and investigate a new graph polynomial of two variables, which is called the SMP polynomial, such that all three vertex versions of the above-mentioned indices can be easily calculated using this polynomial. Moreover, we also define the edge-SMP polynomial, which is the edge version of the SMP polynomial. Various properties of the new polynomials are studied on some basic families of graphs, extremal problems are considered, and several open problems are stated. Then, we focus on the Cartesian product, and we show how the (edge-)SMP polynomial of the Cartesian product of n graphs can be calculated using the (weighted) SMP polynomials of its factors.
Keywords: SMP polynomial, edge-SMP polynomial, Cartesian product, Szeged index, Mostar index, PI index
Published in DKUM: 09.02.2024; Views: 262; Downloads: 20
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