## Abstract

The Turán number of a graph *H*, denoted by *ex*(*n, H*), is the maximum number of edges in any graph on *n* vertices which does not contain *H* as a subgraph. Let *P _{k}* denote the path on

*k*vertices and let

*mP*denote

_{k}*m*disjoint copies of

*P*. Bushaw and Kettle [

_{k}*Turán numbers of multiple paths and equibipartite forests*, Combin. Probab. Comput. 20 (2011) 837–853] determined the exact value of

*ex*(

*n, kP*) for large values of

_{ℓ}*n*. Yuan and Zhang [

*The Turán number of disjoint copies of paths*, Discrete Math. 340 (2017) 132–139] completely determined the value of

*ex*(

*n, kP*

_{3}) for all

*n*, and also determined

*ex*(

*n, F*), where

_{m}*F*is the disjoint union of

_{m}*m*paths containing at most one odd path. They also determined the exact value of

*ex*(

*n, P*

_{3}∪

*P*

_{2}

_{ℓ}_{+1}) for

*n*≥ 2

*ℓ*+ 4. Recently, Bielak and Kieliszek [

*The Turán number of the graph*2

*P*

_{5}, Discuss. Math. Graph Theory 36 (2016) 683–694], Yuan and Zhang [

*Turán numbers for disjoint paths*, arXiv:1611.00981v1] independently determined the exact value of

*ex*(

*n,*2

*P*

_{5}). In this paper, we show that

*ex*(

*n,*2

*P*

_{7}) = max{[

*n,*14, 7], 5

*n*− 14} for all

*n*≥ 14, where [

*n,*14, 7] = (5

*n*+ 91 +

*r*(

*r*− 6))

*/*2,

*n*− 13 ≡

*r*(mod 6) and 0 ≤

*r <*6.