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Exact Formula Computing The Wiener Index On Rows Of Unit Cells Of The Diamond Cubic Grid Connected In A Row

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2019Publisher:Al-Quds Open UniversityJournal:المجلة الفلسطينية للتكنولوجيا والعلوم التطبيقية

Authors: Dr. Hamzeh Mujahed; Dr. Benedek Nagy;

doi: 10.33977/2106-000-002-007 , 10.5281/zenodo.2576339 , 10.5281/zenodo.2582918 , 10.5281/zenodo.2576338 , 10.5281/zenodo.2582919

Exact Formula Computing The Wiener Index On Rows Of Unit Cells Of The Diamond Cubic Grid Connected In A Row

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Abstract

The Wiener Index, the sum of distances between all pairs of vertices in a connected graph, is a graph invariant much studied in both mathematical and chemical literature.Topological graph indices are introduced as mathematical tools for molecule descriptions. Recently, they were computed not only for graphs representing molecules, but for other regular structured graphs including some 2 and 3 dimensional structures. The Carbon atoms in the diamond are arranged in a well defined structure. In this paper, the graph of this structure is analysed, especially, the connected part of a sequence of unit cells. The Wiener index, as the sum of the distances for every pair of atoms is computed, a closed formula depending only on the number of unit cells is proven.

Related Organizations

Eastern Mediterranean University
Cyprus
Al-Quds Open University
Palestinian-administered areas

Keywords

Wiener Index, Shortest Paths, Diamond Grid, Body-Centered Cubic Grid, Face-Centered Cubic, Non-Traditional Grids

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