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
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; } |
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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) |
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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) |
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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) |
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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) ?> |
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Output:
Star Graph
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