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On size of $k$-stepwise irregular graphs and their degree based indices | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 01 اسفند 1404 اصل مقاله (385.58 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.31308.2812 | ||
| نویسندگان | ||
| Yaser Alizadeh1؛ Sandi Klavžar* 2، 3، 4؛ Javaher Langari1 | ||
| 1Department of Mathematics, Hakim Sabzevari University, Sabzevar, Iran | ||
| 2Faculty of Mathematics and Physics, University of Ljubljana, Slovenia | ||
| 3Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia | ||
| 4Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia | ||
| چکیده | ||
| A graph $G$ is $k$-stepwise irregular if $|d_G(u)-d_G(v)|= k$ holds for every edge $uv$ of $G$. It is proved that for such a graph $m(G) \leq (n(G)^2 - k^2)/4$ holds, where the equality holds if and only if $G\cong K_{\frac{n(G)+k}{2},\frac{n(G)-k}{2}}$. Using this result, sharp lower and upper bounds are derived for Zagreb (co)indices, the Sombor index, and the Randi'c index of $k$-stepwise irregular graphs. | ||
| کلیدواژهها | ||
| stepwise irregular graph؛ Zagreb index, Sombor index, Randi\' c index | ||
| مراجع | ||
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