Newspaper boy problem: Dijkstra's/Shortest Path Algorithm implementation in C++

#include <iostream>
using namespace std;

class graph{
int vertices=0;
int **adj;
public:
graph(){
cout<<"Enter total no of lanes ";
cin>>vertices;
}
int read_G();
void path(int);
void path_rep_ver(int);
};

int graph::read_G(){
adj = new int*[vertices];
for(int i = 0; i < vertices; ++i) {
   adj[i] = new int[vertices];
}

for(int i=0;i<vertices;i++)
for(int j=0;j<vertices;j++)
adj[i][j]=999;

for(int r=0;r<vertices;r++)
{

for(int c=r+1;c<vertices;c++)
{   cout<<"enter distance between lane "<<r+1<<" and "<<c+1<<" : ";
cin>>adj[r][c];
adj[c][r]=adj[r][c]; // Creates cost matrix
}
}

return 0;
}

void graph::path(int start){
int visited[vertices],min,count=1,i,distance=0,temp=0;
for(i=0;i<vertices;i++){
visited[i]=0;
}
cout<<"Visits lane :"<<start+1;
visited[start]=1;
while(count!=vertices) {
min=adj[start][start];
for(i=0;i<vertices;i++)
if(min>adj[start][i] && !visited[i]){
min=adj[start][i];
temp=i;
}

visited[temp]=1;
count++;
cout<<" --> "<<temp+1;
distance=distance+min;
start=temp;

}
cout<<endl<<"Total minimum distance traveled :"<<distance;
}

int main() {
int start;
graph g;
g.read_G();
cout<<"Enter the starting point (Starting lane):";
cin>>start;
g.path(--start);
return 0;
}