Check for star graph - GeeksforGeeks

You are given an n * n matrix which represent a graph with n-vertices, check whether the input matrix represent a star graph or not.

Example:

Input : Mat[][] = {{0, 1, 0},
                   {1, 0, 1},
                   {0, 1, 0}}
Output : Star graph

Input : Mat[][] = {{0, 1, 0},
                   {1, 1, 1},
                   {0, 1, 0}}
Output : Not a Star graph

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Star graph : Star graph is a special type of graph in which n-1 vertices have degree 1 and a single vertex have degree n – 1. This looks like that n – 1 vertices are connected to a single central vertex. A star graph with total n – vertex is termed as Sn.

Here is an illustration for the star graph :

Approach : Just traverse whole matrix and record the number of vertices having degree 1 and degree n-1. If number of vertices having degree 1 is n-1 and number of vertex having degree n-1 is 1 then our graph should be a star graph other-wise it should be not.
Note:

For S1, there must be only one vertex with no edges.
For S2, there must be two vertices each with degree one or can say, both are connected by a single edge.
For Sn (n>2) simply check the above explained criteria.

C++

// CPP to find whether given graph is star or not 
#include<bits/stdc++.h> 
using namespace std; 
  
// define the size of incidence matrix 
#define size 4 
  
// function to find star graph 
bool checkStar(int mat[][size]) 
{ 
    // initialize number of vertex 
    // with deg 1 and n-1 
    int vertexD1 = 0, vertexDn_1 = 0; 
  
    // check for S1 
    if (size == 1) 
        return (mat[0][0] == 0); 
      
    // check for S2 
    if (size == 2)     
       return (mat[0][0] == 0 && mat[0][1] == 1 &&  
               mat[1][0] == 1 && mat[1][1] == 0 ); 
  
    // check for Sn (n>2) 
    for (int i = 0; i < size; i++) 
    { 
        int degreeI = 0; 
        for (int j = 0; j < size; j++) 
            if (mat[i][j]) 
                degreeI++; 
  
        if (degreeI == 1) 
            vertexD1++; 
        else if (degreeI == size-1) 
            vertexDn_1++; 
    } 
      
    return (vertexD1 == (size-1) &&  
            vertexDn_1 == 1); 
} 
  
// driver code 
int main() 
{ 
    int mat[size][size] = { {0, 1, 1, 1}, 
                            {1, 0, 0, 0}, 
                            {1, 0, 0, 0}, 
                            {1, 0, 0, 0}}; 
  
    checkStar(mat) ? cout << "Star Graph" :  
                     cout << "Not a Star Graph"; 
    return 0; 
} 

Java

// Java program to find whether  
// given graph is star or not 
import java.io.*; 
  
class GFG 
{ 
    // define the size of 
    // incidence matrix 
    static int size = 4; 
      
    // function to find 
    // star graph 
    static boolean checkStar(int mat[][]) 
    { 
        // initialize number of  
        // vertex with deg 1 and n-1 
        int vertexD1 = 0,  
            vertexDn_1 = 0; 
      
        // check for S1 
        if (size == 1) 
            return (mat[0][0] == 0); 
          
        // check for S2 
        if (size == 2)  
        return (mat[0][0] == 0 &&  
                mat[0][1] == 1 &&  
                mat[1][0] == 1 && 
                mat[1][1] == 0); 
      
        // check for Sn (n>2) 
        for (int i = 0; i < size; i++) 
        { 
            int degreeI = 0; 
            for (int j = 0; j < size; j++) 
                if (mat[i][j] == 1) 
                    degreeI++; 
      
            if (degreeI == 1) 
                vertexD1++; 
            else if (degreeI == size - 1) 
                vertexDn_1++; 
        } 
          
        return (vertexD1 == (size - 1) &&  
                vertexDn_1 == 1); 
    } 
      
    // Driver code 
    public static void main(String args[]) 
    { 
        int mat[][] = {{0, 1, 1, 1}, 
                       {1, 0, 0, 0}, 
                       {1, 0, 0, 0}, 
                       {1, 0, 0, 0}}; 
      
        if (checkStar(mat)) 
            System.out.print("Star Graph");  
        else
            System.out.print("Not a Star Graph"); 
    } 
} 
  
// This code is contributed by  
// Manish Shaw(manishshaw1) 

Python3

# Python to find whether  
# given graph is star 
# or not 
  
# define the size  
# of incidence matrix 
size = 4
  
# def to  
# find star graph 
def checkStar(mat) : 
  
    global size 
      
    # initialize number of  
    # vertex with deg 1 and n-1 
    vertexD1 = 0
    vertexDn_1 = 0
  
    # check for S1 
    if (size == 1) : 
        return (mat[0][0] == 0) 
      
    # check for S2 
    if (size == 2) : 
        return (mat[0][0] == 0 and 
                mat[0][1] == 1 and 
                mat[1][0] == 1 and 
                mat[1][1] == 0) 
  
    # check for Sn (n>2) 
    for i in range(0, size) : 
  
        degreeI = 0
        for j in range(0, size) : 
            if (mat[i][j]) : 
                degreeI = degreeI + 1
  
        if (degreeI == 1) : 
            vertexD1 = vertexD1 + 1
  
        elif (degreeI == size - 1): 
            vertexDn_1 = vertexDn_1 + 1
      
    return (vertexD1 == (size - 1) and 
            vertexDn_1 == 1) 
  
# Driver code 
mat = [[0, 1, 1, 1], 
       [1, 0, 0, 0], 
       [1, 0, 0, 0], 
       [1, 0, 0, 0]] 
   
if(checkStar(mat)) : 
    print ("Star Graph") 
else : 
    print ("Not a Star Graph") 
      
# This code is contributed by  
# Manish Shaw(manishshaw1) 

C#

// C# to find whether given 
// graph is star or not 
using System; 
  
class GFG 
{ 
    // define the size of 
    // incidence matrix 
    static int size = 4; 
      
    // function to find 
    // star graph 
    static bool checkStar(int [,]mat) 
    { 
        // initialize number of  
        // vertex with deg 1 and n-1 
        int vertexD1 = 0, vertexDn_1 = 0; 
      
        // check for S1 
        if (size == 1) 
            return (mat[0, 0] == 0); 
          
        // check for S2 
        if (size == 2)  
        return (mat[0, 0] == 0 &&  
                mat[0, 1] == 1 &&  
                mat[1, 0] == 1 && 
                mat[1, 1] == 0); 
      
        // check for Sn (n>2) 
        for (int i = 0; i < size; i++) 
        { 
            int degreeI = 0; 
            for (int j = 0; j < size; j++) 
                if (mat[i, j] == 1) 
                    degreeI++; 
      
            if (degreeI == 1) 
                vertexD1++; 
            else if (degreeI == size - 1) 
                vertexDn_1++; 
        } 
          
        return (vertexD1 == (size - 1) &&  
                vertexDn_1 == 1); 
    } 
      
    // Driver code 
    static void Main() 
    { 
        int [,]mat = new int[4, 4]{{0, 1, 1, 1}, 
                                   {1, 0, 0, 0}, 
                                   {1, 0, 0, 0}, 
                                   {1, 0, 0, 0}}; 
      
        if (checkStar(mat)) 
            Console.Write("Star Graph");  
        else
            Console.Write("Not a Star Graph"); 
    } 
} 
// This code is contributed by  
// Manish Shaw(manishshaw1) 

PHP

<?php 
// PHP to find whether  
// given graph is star 
// or not 
  
// define the size  
// of incidence matrix 
$size = 4; 
  
// function to  
// find star graph 
function checkStar($mat) 
{ 
    global $size; 
      
    // initialize number of  
    // vertex with deg 1 and n-1 
    $vertexD1 = 0; 
    $vertexDn_1 = 0; 
  
    // check for S1 
    if ($size == 1) 
        return ($mat[0][0] == 0); 
      
    // check for S2 
    if ($size == 2)  
    return ($mat[0][0] == 0 &&  
            $mat[0][1] == 1 &&  
            $mat[1][0] == 1 &&  
            $mat[1][1] == 0 ); 
  
    // check for Sn (n>2) 
    for ($i = 0; $i < $size; $i++) 
    { 
        $degreeI = 0; 
        for ($j = 0; $j < $size; $j++) 
            if ($mat[$i][$j]) 
                $degreeI++; 
  
        if ($degreeI == 1) 
            $vertexD1++; 
        else if ($degreeI == $size - 1) 
            $vertexDn_1++; 
    } 
      
    return ($vertexD1 == ($size - 1) &&  
            $vertexDn_1 == 1); 
} 
  
// Driver code 
$mat = array(array(0, 1, 1, 1), 
             array(1, 0, 0, 0), 
             array(1, 0, 0, 0), 
             array(1, 0, 0, 0)); 
  
if(checkStar($mat)) 
    echo ("Star Graph"); 
else
    echo ("Not a Star Graph"); 
      
// This code is contributed by  
// Manish Shaw(manishshaw1) 
?> 

Output:

Star Graph

My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

PHP

Recommended Posts: