@article{Article_13,

title = {On The Edge Double Roman Domination Number of Planar Graph},

journal = {Communications in Combinatorics, Cryptography & Computer Science},

volume = {2021},

issue = {2},

issn = { 2783-5456 },

year = {2021},

url = {http://cccs.sgh.ac.ir/Articles/2021/issue 2/2-1-on_the_edge_double_roman_domination_number_of_planar_graph-1637956327.pdf},

author = {Mina Valinavaz},

keywords = {Double Roman dominating function, Double Roman domination number, Edge double Roman dominating function, Edge double Roman domination number.},

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.}

};