Working Paper Article Version 1 This version is not peer-reviewed

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

Version 1 : Received: 3 April 2021 / Approved: 5 April 2021 / Online: 5 April 2021 (12:20:10 CEST)

How to cite: Şahin, B.; Şahin, A. ve-degree, ev-degree and First Zagreb Index Entropies of Graphs. Preprints 2021, 2021040117 Şahin, B.; Şahin, A. ve-degree, ev-degree and First Zagreb Index Entropies of Graphs. Preprints 2021, 2021040117

Abstract

Chellali et al. introduced two degree concepts, ve-degree and ev-degree (Chellali et al, 2017). The ve-degree of a vertex 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.

Subject Areas

ve-degree, ev-degree, entropy, information functional

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