Check For Star Graph

A graph is given; we have to check the given graph is a star graph or not.

By traversing the graph, we have to find the number of vertices has degree one, and number of vertices, whose degree is n-1. (Here n is the number of vertices in the given graph). When the number of vertices with degree 1 is n-1 and a number of vertices with a degree (n-1) is one, then it is a star graph.

Input and Output

Input:
The adjacency matrix:
0 1 1 1
1 0 0 0
1 0 0 0
1 0 0 0

Output:
It is a star graph.

Algorithm

checkStarGraph(graph)

Input: The given Graph.

Output: True when the graph is a star graph.

Begin
   degOneVert := 0 and degNminOneGraph := 0
   if graph has only one vertex, then
      return true, if there is no self-loop
   else if graph has two vertices, then
      return true if there is only one vertex between two vertices
   else
      for all vertices i in the graph, do
         degree := 0
         for all vertices j, adjacent with i, do
            degree := degree + 1
         done
         if degree = 1, then
            degOneVert := degOneVert + 1
         else if degree = n-1, then
            degNminOneGraph := degNminOneGraph + 1
      done

   if degOneVert = n-1, and degNminOneGraph = 1, then
      return true
   otherwise return false
End

Example

#include<iostream>
#define NODE 4
using namespace std;

int graph[NODE][NODE] = {
   {0, 1, 1, 1},
   {1, 0, 0, 0},
   {1, 0, 0, 0},
   {1, 0, 0, 0}
};

bool checkStarGraph() {
   int degOneVert = 0, degVert = 0;    //initially vertex with degree 1 and with degree n - 1 are 0
   if (NODE == 1)    //when there is only one node
      return (graph[0][0] == 0);

   if (NODE == 2)  
      return (graph[0][0] == 0 && graph[0][1] == 1 && graph[1][0] == 1 && graph[1][1] == 0 );

   for (int i = 0; i < NODE; i++) {    //for graph more than 2
      int degree = 0;
      for (int j = 0; j < NODE; j++)    //count degree for vertex i
         if (graph[i][j])
            degree++;
      if (degree == 1)
         degOneVert++;
      else if (degree == NODE-1)
         degVert++;
   }
   //when only vertex of degree n-1, and all other vertex of degree 1, it is a star graph
   return (degOneVert == (NODE-1) && degVert == 1);
}

int main() {
   if(checkStarGraph())
      cout << "It is a star graph.";
   else
     cout << "It is not a star graph.";
}

Output

It is a star graph.