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# Check for star graph

• Difficulty Level : Basic
• Last Updated : 03 May, 2021

You are given an n * n matrix which represents a graph with n-vertices, check whether the input matrix represents 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 n – 1 vertex is 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``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

 `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)``?>`

## Javascript

 ``

Output:

`Star Graph`

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