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A study on some properties of leap graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 11، دوره 5، شماره 1، شهریور 2020، صفحه 9-17 اصل مقاله (377.44 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2019.26430.1108 | ||
| نویسندگان | ||
| Ahmed M Naji* 1؛ B. Davvaz2؛ Sultan S. Mahde3؛ N.D. Soner3 | ||
| 1Department of Mathematics, University of Mysore, Mysusu, India | ||
| 2Department of Mathematics, Yazd University, Yazd, Iran | ||
| 3Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore - 570 006, India | ||
| چکیده | ||
| In a graph $G$, the first and second degrees of a vertex $v$ are equal to the number of their first and second neighbors and are denoted by $d(v/G)$ and $d_2(v/G)$, respectively. The first, second and third leap Zagreb indices are the sum of squares of second degrees of vertices of $G$, the sum of products of second degrees of pairs of adjacent vertices in $G$ and the sum of products of first and second degrees of vertices of $G$, respectively. In this paper, we initiate in studying a new class of graphs depending on the relationship between first and second degrees of vertices and is so-called a leap graph. Some properties of the leap graphs are presented. All leap trees and $\{C_3, C_4\}$-free leap graphs are characterized. | ||
| کلیدواژه‌ها | ||
| Distance-degrees (of vertices)؛ leap Zagreb indices؛ leap graphs | ||
| مراجع | ||
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