6/22/2023 0 Comments Math graphDetecting cycles in an undirected graph.Minimum spanning tree for un-weighted graph.Or, $a \rightarrow d \rightarrow e \rightarrow b \rightarrow c$ Or, $a \rightarrow b \rightarrow e \rightarrow d \rightarrow c$ Or, $a \rightarrow e \rightarrow b \rightarrow d \rightarrow c$ Or, $a \rightarrow d \rightarrow b \rightarrow e \rightarrow c$ $a \rightarrow b \rightarrow e \rightarrow d \rightarrow c$ $a \rightarrow b \rightarrow d \rightarrow e \rightarrow c$ Remove c from queue and mark it as “Visited”. Remove e from queue and mark it as “Visited”. Remove d from queue and mark it as “Visited”. Remove b from queue, mark it as “Visited”, put its “Ready” neighbor c at end of queue and mark c as “Waiting”. Remove a from queue, mark it as “Visited”.Īdd a’s neighbors in “Ready” state b, d and e to end of queue and mark them as “Waiting”. Put a in queue and change its status to “Waiting”. Initialize status of all vertices to “Ready”. ![]() Let us take a graph (Source vertex is ‘a’) and apply the BFS algorithm to find out the traversal order. Remove the first vertex from the queue and mark it as “Visited”.Īdd to the rear of queue all neighbors of the removed vertex whose status is “Ready”. Repeat the following two steps until queue is empty − Put source vertex in a queue and change its status to “Waiting”. Initialize status of all nodes as “Ready”. The concept is to visit all the neighbor vertices before visiting other neighbor vertices of neighbor vertices. The BFS traversal terminates when every vertex of the graph has been visited. Then we start from the level-1 vertices and apply the same method on every level-1 vertex and so on. After visiting, we mark the vertices as "visited," and place them into level-1. Then we visit all the vertices that are the neighbors of $X$. There are mainly two ways to traverse a graph.īreadth First Search (BFS) starts at starting level-0 vertex $X$ of the graph $G$. Graph traversal is the problem of visiting all the vertices of a graph in some systematic order. Some applications of graph coloring include − Hence, the chromatic number of the graph is 3. Hence, we could color the graph by 3 colors. Then vertex $c$ is colored as red as no adjacent vertex of $c$ is colored red. As the adjacent vertices of vertex a are again adjacent, vertex $b$ and vertex $d$ are colored with different color, green and blue respectively. In the above figure, at first vertex $a$ is colored red. ![]() Repeat this step until all the vertices are colored. If all the adjacent vertices are colored with this color, assign a new color to it. Step 3 − Choose the next vertex and color it with the lowest numbered color that has not been colored on any vertices adjacent to it. Step 2 − Choose the first vertex and color it with the first color. Step 1 − Arrange the vertices of the graph in some order. The steps required to color a graph G with n number of vertices are as follows − Graph coloring problem is a NP Complete problem. The smallest number of colors required to color a graph G is called its chromatic number of that graph. The objective is to minimize the number of colors while coloring a graph. Graph coloring is the procedure of assignment of colors to each vertex of a graph G such that no adjacent vertices get same color.
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