Original Research Article

Article volume = 2021 and issue = 2

Pages: 97–103

Article publication Date: November, 1, 2021

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# On The Edge Double Roman Domination Number of Planar Graph

#### Mina Valinavaz

Department of Mathematics, Azarbaijan Shahid Madani University Tabriz, I.R. Iran.

##### Abstract:

An edge double Roman dominating function (EDRDF) on a graph G is a function f : E(G) ! f0, 1, 2, 3g satisfying the condition that such that every edge e with f(e) = 0, is adjacent to at least two edge e, e0 for which f(e) = f(e0) = 2 or one edge e00 with f(e00) = 3, and if f(e) = 1, then edge e must have at least one neighbor e0 with f(e0) > 2. The Edge double Roman dominating number of G, denoted by 0 dR(G), is the minimum weight w(f) = P e2E(G) f(e) of an edge double Roman dominating function f of G. In this paper, we introduction some results on the edge double Roman domination number of a graph. Also, we provide some upper and lower bounds for the edge double Roman domination number of graphs.

##### Keywords:

Double Roman dominating function, Double Roman domination number, Edge double Roman dominating function, Edge double Roman domination number.

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##### Cite this article as:

- Mina Valinavaz, On The Edge Double Roman Domination Number of Planar Graph, Communications in Combinatorics, Cryptography & Computer Science, 2021(2), PP.97–103, 2021
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