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Entire Wiener index of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 20، دوره 7، شماره 2، اسفند 2022، صفحه 227-245 اصل مقاله (468.87 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2021.27234.1217 | ||
| نویسندگان | ||
| Ismail Naci CANGUL* 1؛ Anwar Saleh2؛ Akram Alqesmah3؛ Hanaa Alashwali2 | ||
| 1Uludag University Faculty of Arts and Science Department of Mathematics Gorukle, 16059 Bursa/Turkey | ||
| 2Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia | ||
| 3Department of Mathematics, University of Aden, Yemen | ||
| چکیده | ||
| Topological indices are graph invariants computed usually by means of the distances or degrees of vertices of a graph. In chemical graph theory, a molecule can be modeled by a graph by replacing atoms by the vertices and bonds by the edges of this graph. Topological graph indices have been successfully used in determining the structural properties and in predicting certain physicochemical properties of chemical compounds. Wiener index is the oldest topological index which can be used for analyzing intrinsic properties of a molecular structure in chemistry. The Wiener index of a graph $G$ is equal to the sum of distances between all pairs of vertices of $G$. Recently, the entire versions of several indices have been introduced and studied due to their applications. Here we introduce the entire Wiener index of a graph. Exact values of this index for trees and some graph families are obtained, some properties and bounds for the entire Wiener index are established. Exact values of this new index for subdivision and $k$-subdivision graphs and some graph operations are obtained. | ||
| کلیدواژهها | ||
| topological graph index؛ Wiener index؛ entire Wiener index | ||
| مراجع | ||
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