free(): invalid pointer error on vector.push_back() - c++

Question

My code gives me free(): invalid pointer error (I don't call free, so my understanding is that it has something to do with how vectors operate internally). I am beginner to C++, so though I checked other answers to similar questions, I fail to see what exactly causes the issue.
I have a grid graph (i.e. vertex is connected with its 4-neighbors). Some vertices hold a special value, which is written done in a file in a form:
row columns value
The code:
graph::graph(const char *file_name) {
ifstream infile(file_name);
istringstream iss;
int R = 2; // number of rows
int C = 4; // number of columns
for (int i=0; i<R*C; i++) add_vertex(i+1);
adj = new std::vector<edge*>[R*C]; // adjacency list
// add all edges to the grid
for (int r=0; r<R; r++) {
for (int c=0; c<C; c++) {
if (c!=C-1) add_edge(vertices[r*C+c], vertices[r*C+(c+1)]);
if (r!=R-1) add_edge(vertices[r*C+c], vertices[(r+1)*C+c]);
}
}
int P = 2; // number of vertices holding a special value
for (int i=0; i<P; i++) {
getline(infile, line);
iss.str(line);
iss >> r >> c >> p;
vertices[r*C+c]->set_value(p);
p_vertices.push_back(vertices[r*C+c]);
iss.clear();
}
void graph::add_vertex(int v) {
auto *vert = new vertex(v);
vertices.push_back(vert);
}
void graph::add_edge(vertex *v, vertex *u) {
edge e = std::make_tuple(v, u, 1);
adj[v->get_id()].push_back(&e);
adj[u->get_id()].push_back(&e);
}
Header:
#include "vertex.h"
typedef std::tuple<vertex*, vertex*, int> edge;
class graph {
private:
std::vector<vertex*> vertices; // all vertices
std::vector<vertex*> p_vertices; // vertices with a special value
std::vector<edge*> *adj; // adjacency list
public:
explicit graph(const char *file_name);
void add_vertex(int v);
void add_edge(vertex *v, vertex *u);
};
Header for a vertex:
#include <string>
#include <vector>
class vertex {
private:
int id;
int val;
public:
explicit vertex(int id) {
this->id = id;
this->val = 0;
};
int get_id() { return id; };
void set_value(int p) { val = p; };
};
Example input:
0 0 1
1 2 3
The error disappears if I comment out this line:
p_vertices.push_back(vertices[r*C+c]);
And remains even if I try to change p_vertices to std::vector<int> instead of std::vector<vertex*> (and use p_vertices.push_back(r*C+c)).
Thanks for any hints on how to fix the error.