Kevin is a computer science enthusiast exploring the intricacies of graph theory. He is actively developing a program that, given an adjacency matrix, calculates the chromatic number of an undirected graph. The chromatic number is the minimum count of colors needed to color the graph vertices, ensuring neighboring vertices have distinct colors.Your role is to support Kevin in implementing this algorithm, facilitating his understanding of chromatic numbers and their application in practical problem-solving.Input format :The first line contains an integer v, representing the number of vertices in the graph.The next v lines contain the adjacency matrix of the graph, where each line contains v space-separated integers (0 or 1).Output format :The output prints "Chromatic Number of the graph is: " followed by an integer representing the chromatic number of the graph.Refer to the sample output for the formatting specifications.Code constraints :1 ≤ v ≤ 50Sample test cases :Input 1 :40 1 1 11 0 1 01 1 0 11 0 1 0Output 1 :Chromatic Number of the graph is: 3Input 2 :50 1 0 1 01 0 1 0 10 1 0 1 01 0 1 0 10 1 0 1 0Output 2 :Chromatic Number of the graph is: 2Input 3 :50 1 1 0 01 0 1 1 01 1 0 1 10 1 1 0 10 0 1 1 0Output 3 :Chromatic Number of the graph is: 3write an accurate code for this problem in c following given input and output formats

Sure, I can help you with that. Here's an accurate code in C to solve the problem:

#include <stdio.h>

#define MAX_VERTICES 50

int graph[MAX_VERTICES][MAX_VERTICES];
int chromaticNumber = 0;

int isSafe(int v, int color, int colors[])
{
    for (int i = 0; i < v; i++)
    {
        if (graph[v][i] && color == colors[i])
            return 0;
    }
    return 1;
}

void graphColoringUtil(int v, int colors[])
{
    if (v == MAX_VERTICES)
    {
        int maxColor = 0;
        for (int i = 0; i < MAX_VERTICES; i++)
        {
            if (colors[i] > maxColor)
                maxColor = colors[i];
        }
        if (maxColor < chromaticNumber)
            chromaticNumber = maxColor;
        return;
    }

    for (int c = 1; c <= chromaticNumber + 1; c++)
    {
        if (isSafe(v, c, colors))
        {
            colors[v] = c;
            graphColoringUtil(v + 1, colors);
            colors[v] = 0;
        }
    }
}

int main()
{
    int v;
    scanf("%d", &v);

    for (int i = 0; i < v; i++)
    {
        for (int j = 0; j < v; j++)
        {
            scanf("%d", &graph[i][j]);
        }
    }

    int colors[MAX_VERTICES] = {0};
    chromaticNumber = v;

    graphColoringUtil(0, colors);

    printf("Chromatic Number of the graph is: %d\n", chromaticNumber);

    return 0;
}

This code takes the input in the specified format, where the first line represents the number of vertices (v) and the next v lines represent the adjacency matrix of the graph. It then calculates the chromatic number using a backtracking algorithm and prints the result in the specified output format.