91影视

$ClassP:P$is a class of languages that are decidable in polynomial time on a deterministic single 鈥� tape Turing 鈥� machine.

Specified language, a triangle is an undirected graph is a$3--clique$.Now we have to show that $TRIANGLE鈭�P$

Let $AbetheTuringmachinethatdecidesTRIANGLE$ is polynomial time$A$can be described as follows:

:$A=\text{'}\text{'}oninput$$G<V,E>$

$V$ denotes set of vertices of the graph$G$ .

$E$ denotes set of edges of the graph$G$ .

For $u,v,w鈭�V$ and $u<v<w$we enumerate all triples $<u,v,w>$.Check whether all three edges $\left(u,v\right)(v,w)$exist in $E$or not. If exist then accept.Otherwise reject.鈥�

Enumeration of all triple require$0\left(\right|v{|}^3)$time. Checking whether all three edges belong to $E$ take $0\left(\right|E\left|\right)$time.Overall time is $0\left(\right|V{|}^3\left|E\right|)$which is polynomial in the length of the inlets. Therefore$TRIANGLE鈭�P$ . Three edges connection over base on the theory of polynomial show the length of inplet..