1. bookAHEAD OF PRINT
Journal Details
License
Format
Journal
eISSN
2083-5892
First Published
13 Apr 2013
Publication timeframe
4 times per year
Languages
English
access type Open Access

Bounds on the Total Double Roman Domination Number of Graphs

Published Online: 05 Aug 2021
Volume & Issue: AHEAD OF PRINT
Page range: -
Received: 03 Nov 2020
Accepted: 07 Jun 2021
Journal Details
License
Format
Journal
eISSN
2083-5892
First Published
13 Apr 2013
Publication timeframe
4 times per year
Languages
English
Abstract

Let G be a simple graph with no isolated vertex and let γtdR(G) be the total double Roman domination number of G. In this paper, we present lower and upper bounds on γtdR (G) of a graph G in terms of the order, open packing number and the numbers of support vertices and leaves, and we characterize all extremal graphs. We also prove that for any connected graph G of order n with minimum degree at least two, γtdR (G) ≤ 4n3\left\lfloor {{{4n} \over 3}} \right\rfloor.

Keywords

MSC 2010

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