Preprint Article Version 1 This version is not peer-reviewed

# On Total Vertex-Edge Domination

Version 1 : Received: 10 July 2018 / Approved: 11 July 2018 / Online: 11 July 2018 (10:52:10 CEST)

How to cite: Şahin, B.; Şahin, A. On Total Vertex-Edge Domination. Preprints 2018, 2018070195 (doi: 10.20944/preprints201807.0195.v1). Şahin, B.; Şahin, A. On Total Vertex-Edge Domination. Preprints 2018, 2018070195 (doi: 10.20944/preprints201807.0195.v1).

## Abstract

A novel domination invariant defined by Boutrig and Chellali in the recent: total vertex-edge domination. In this paper we obtain an improved upper bound of total vertex edge-domination number of a tree. If  is a connected tree with order , then  with  and we characterize the trees attaining this upper bound. Furthermore we provide a characterization of trees  with

## Subject Areas

domination, vertex-edge domination, total vertex-edge domination