bipartite Samsung

/*The function takes an adjacency matrix representation of the graph (g)
and an integer(v) denoting the no of vertices as its arguments.
You are required to complete below method */

bool bfsutil(int a[][MAX], int V,int r){
    string color[V+1];
    for(int i=0; i<V; i++)
            color[i]="white";

    queue<int>q;
    q.push(r);
    color[r]="red";
    while(!q.empty()){
        int node=q.front();
        q.pop();
        for(int j=0; j<V; j++){
            if(a[node][j]==1){
                if(color[j]=="white"){
                    q.push(j);
                    if(color[node]=="red") color[j]="blue";
                    else color[j]="red";
                }
                else{
                    if(color[j]==color[node] || node==j) return false;
                }
            }
        }
    }
    return true;
}


bool isBipartite(int a[][MAX],int V){
    if(V==1) {
        if(a[0][0]) return false;
    }
    for(int i=0; i<V; i++){
        if(bfsutil(a,V,i)) continue;
        else
            return false;
    }
    return true;
}