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An inequality for the Mostar index of line graphs of trees | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 22 بهمن 1403 اصل مقاله (487.36 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30201.2356 | ||
| نویسندگان | ||
| Muhammad Shoaib Sardar1؛ Naveed Iqbal* 2؛ Sharaft Hussain3؛ Safyan Mukhtar4؛ Wael W. Mohammed2 | ||
| 1College of Mathematical Sciences, Harbin Engineering University, Harbin, PR China | ||
| 2Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia | ||
| 3Department of Mathematics Women University of Azad Jammu and Kashmir Bagh, India | ||
| 4General Administration of Preparatory Year, King Faisal University, Al-Ahsa 31982, Saudi Arabia | ||
| چکیده | ||
| Consider a simple connected graph G with the vertex set V (G) and edge set E(G). The Mostar index M◦(G) of G is defined as M◦(G) = e=xy∈E(G) |nx − ny|, where nx and ny represent the number of vertices that lie closer to x than to y and the number of vertices that lie closer to y than to x, respectively. In this paper, we prove that if G is a tree, then M◦(LG) < M◦(G), where LG is the line graph. In order to provide an example supporting this result, we develop three algorithms (and implement them using Python) to calculate the Mostar index of trees of order at most 8 and their line graphs. | ||
| کلیدواژهها | ||
| Mostar Index؛ line graph؛ trees؛ graph transformation؛ Algorithmic graph analysis | ||
| مراجع | ||
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