@article{Article_46,

title = {Efficient Dominating Set in Fullerene Graph},

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

volume = {2022},

issue = {2},

issn = { 2783-5456 },

year = {2022},

url = {http://cccs.sgh.ac.ir/Articles/2022/issue 2/2-10-EfficientDominatingSetinFullereneGraph.pdf},

author = {Fatemeh Mirzaei and Afshin Behmaram},

keywords = {perfect star packing, fullerene, dominating set.},

abstract = {A Fullerene graph is a 3-regular, 3-connected graph such that all of the Faces is pentagonal and hexagonal.A spanning subgraph of a graph G is called a perfect star packing in G if every component of the spanning subgraph G isomorphic with star graph $K_{1,3}$. The set of Efficient dominating set of the graph G are sets of vertices D such that each vertex in $V(G)-D$ is adjacent to exactly one vertex in D. We prove that the perfect star packing in a fullerene graph G on n vertices will exist if and only if G has an efficient dominating set of cardinality $\dfrac{n}{4}$. Then we show that the size of fullerene graph with an efficient dominating set is 8n.}

};