diff --git a/src/math/lp/lar_term.h b/src/math/lp/lar_term.h
index 2e8117d51..39e2a7d3f 100644
--- a/src/math/lp/lar_term.h
+++ b/src/math/lp/lar_term.h
@@ -22,9 +22,8 @@
 #include "util/map.h"
 
 namespace lp {
-
+// represents a linear expressieon
 class lar_term {
-    // the term evaluates to sum of m_coeffs 
     typedef unsigned lpvar;
     u_map<mpq> m_coeffs;
 public:
diff --git a/src/math/lp/lp_bound_propagator.h b/src/math/lp/lp_bound_propagator.h
index 316fb0914..d6ce5ab93 100644
--- a/src/math/lp/lp_bound_propagator.h
+++ b/src/math/lp/lp_bound_propagator.h
@@ -1,7 +1,7 @@
 /*
   Copyright (c) 2017 Microsoft Corporation
   Author:
-  Nickolaj Bjorner (nbjorner)
+  Nikolaj Bjorner (nbjorner)
   Lev Nachmanson   (levnach)
 */
 #pragma once
@@ -15,16 +15,38 @@ class lp_bound_propagator {
         unsigned           m_row; 
         unsigned           m_index; // in the row
         bool               m_sign; // true if the vertex plays the role of y
-        vector<unsigned>   m_adjacent_edges; // points to the
+        vector<unsigned>   m_out_edges;  // the vertex is x in an x-y edge
+        vector<unsigned>   m_in_edges;  // the vertex is y in an x-y edge
+        vertex() {}
         vertex(unsigned row, unsigned index) : m_row(row), m_index(index) {}
+        unsigned hash() const { return combine_hash(m_row, m_index); }
+        bool operator==(const vertex& v) const { return m_row == v.m_row && m_index == v.m_index; }
+        void add_out_edge(unsigned e) {
+            SASSERT(m_out_edges.contains(e) == false);
+            m_out_edges.push_back(e);
+        }
+        void add_in_edge(unsigned e) {
+            SASSERT(m_in_edges.contains(e) == false);
+            m_in_edges.push_back(e);
+        }
+
     };
 
+    struct vert_hash {  unsigned operator()(const vertex& u) const { return u.hash(); }};
+    struct vert_eq { bool operator()(const vertex& u1, const vertex& u2) const { return u1 == u2; }};
     // an edge can be between columns in the same row or between two different rows in the same column
+    // represents a - b = offset
     struct edge { 
         unsigned  m_a;
         unsigned  m_b;
         impq      m_offset;
+        edge() {}
+        edge(unsigned a, unsigned b, impq offset) : m_a(a), m_b(b), m_offset(offset) {}
+        unsigned hash() const { return combine_hash(m_a, m_b); }
+        bool operator==(const edge& e) const { return m_a == e.m_a && m_b == e.m_b; }
     };
+    struct edge_hash {  unsigned operator()(const edge& u) const { return u.hash(); }};
+    struct edge_eq { bool operator()(const edge& u1, const edge& u2) const { return u1 == u2; }}; 
     vector<vertex> m_vertices;
     vector<edge>   m_edges;
     
@@ -88,20 +110,95 @@ public:
         m_imp.consume(a, ci);
     }
 
+    bool no_duplicate_vertices() const {
+        hashtable<vertex, vert_hash, vert_eq>  verts;
+        for (auto & v : m_vertices) {
+            verts.insert(v);
+        }
+        return verts.size() == m_vertices.size();
+    }
+
+    template <typename K>
+    bool no_duplicate_in_vector(const K& vec) const {
+        hashtable<unsigned, u_hash, u_eq> t;
+        for (unsigned j : vec)
+            t.insert(j);
+        return t.size() == vec.size();
+    }
+
+    bool edge_exits_vertex(unsigned j, const vertex& v) const {
+        const edge & e = m_edges[j];
+        return m_vertices[e.m_b] == v;
+    }
+
+    bool edge_enters_vertex(unsigned j, const vertex& v) const {
+        const edge & e = m_edges[j];
+        return m_vertices[e.m_a] == v;
+    }
+
+    
+    bool vertex_is_ok(unsigned i) const {
+        const vertex& v = m_vertices[i];
+        bool ret = no_duplicate_in_vector(v.m_out_edges)
+            && no_duplicate_in_vector(v.m_in_edges);
+        if (!ret)
+            return false;
+        for (unsigned j : v.m_out_edges) {
+            if (edge_exits_vertex(j, v))
+                return false;
+        }
+        for (unsigned j : v.m_in_edges) {
+            if (edge_enters_vertex(j, v))
+                return false;
+        }
+        return true;
+    }
+    
+    bool vertices_are_ok() const {
+        return no_duplicate_vertices();
+        for (unsigned k = 0; k < m_vertices.size(); k++) {
+            if (!vertex_is_ok(k))
+                return false;
+        }
+        return true;
+    }
+
+    bool no_duplicate_edges() const {
+        hashtable<edge, edge_hash, edge_eq> edges;
+        for (auto & v : m_edges) {
+            edges.insert(v);
+        }
+        return edges.size() == m_edges.size();
+    
+    }
+    
+    bool edges_are_ok() const {
+        return no_duplicate_edges();
+    }
+    
+    bool graph_is_ok() const {
+        return vertices_are_ok() && edges_are_ok();
+    }
+
     void create_initial_xy(unsigned x, unsigned y, unsigned row_index) {
-        impq value;
+        impq offset;
         const auto& row =  lp().get_row(row_index);
         for (unsigned k = 0; k < row.size(); k++) {
             if (k == x || k == y)
                 continue;
             const auto& c = row[k];
-            value += c.coeff() * lp().get_lower_bound(c.var());
+            offset += c.coeff() * lp().get_lower_bound(c.var());
         }
         vertex xv(row_index, x);
         m_vertices.push_back(xv);
         vertex yv(row_index, y);
         m_vertices.push_back(yv);
-        
+        unsigned sz = m_vertices.size();
+        m_edges.push_back(edge(sz - 2, sz - 1, offset));
+        unsigned ei = m_edges.size() - 1;
+        m_vertices[sz - 2].add_out_edge(ei);
+        m_vertices[sz - 1].add_in_edge(ei);
+        SASSERT(graph_is_ok());
         NOT_IMPLEMENTED_YET();
     }