Using some relevant theorems and results of graph theory

two sufficient conditions of digraph with directed Hamiltonian path are studied. That is

let \%D\% be a strongly connected digraph with \%n\%≥2 vertices: 1) Suppose that \%d(x)+d(y)≥2n+1\%

and min{\%d\++(x)+d\+-(y)

d\+-(x)+d\++(y)}\% for every pair of nonadjacent vertices \%x

y∈V(D)\% with a common inneighbour or a common outneighbour

then \%D\% has a directed Hamiltonian path; 2) Suppose that \%d(x)+d(y)≥(5/2)n-5\%

for every pair of nonadjacent vertices \%x

y∈V(D)\% with a common inneighbour or a common outneighbour

then \%D\% has a directed Hamiltonian path. Further

the two sufficient conditions are proved.