ve-degree, ev-degree and First Zagreb Index Entropies of Graphs

Authors : Bünyamin Şahin, Abdulgani Şahin

Pages : 90-101

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Publication Date : 2021-06-01

Article Type : Research

Abstract :Chellali et al. introduced two degree concepts, ve-degree and ev-degree (Chellali et al, 2017). The ve-degree of a vertex v equals to number of different edges which are incident to a vertex from the closed neighborhod of v. Moreover the ev-degree of an edge e=ab equals to the number of vertices of the union of the closed neighborhoods of a and b. The most private feature of these degree concepts is, total number of ve-degrees and total number of ev-degrees equal to first Zagreb index of the graphs for triangle-free graphs. In this paper we introduce ve-degree entropy, ev-degree entropy and investigate the relations between these entropies and the first Zagreb index entropy. Finally we obtain the maximal trees with respect to ve-degree irregularity index.
Keywords : ve-derece, ev-derece, entropi, bilgi fonksiyoneli