On edge distinguishing number of hypercube
Shaobing Zhang · Journal of Heilongjiang Institute of Science and Technology · 2007
Based on the distinguishing number of graph,this paper proposes the edge distinguishing number of graph,and offers the edge distinguishing number of the n-vertex cycle Cn and the n-vertex path Pn.According to the structural properties of the n-dimensional hypercube graph Hn and its p powers Hpn,this paper studies the edge distinguishing number of the n-dimensional hypercube graph Hn,and the p(2)powers of the n-dimensional hypercube graph Hpn,and gives the edge distinguishing number of the n-dimensional hypercube graph,and an upper boundary of the p(2)powers of the n-dimensional hypercube graph,namely,the edge distinguishing number of graph H2 is 3 for n=2,and 2 for n≥3,and the upper boundary of the edge distinguishing number of graph Hpn is 3 for n≥4 and n≥p2.