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What graph traversal algorithm uses a queue to keep track of vertices which need to be processed?
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∙ 10y ago
Breadth-first search
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∙ 10y ago
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How many minimum edges in a Cyclic graph with n vertices?
The term "cyclic graph" is not well-defined. If you mean a graph that is not acyclic, then the answer is 3. That would be the union of a complete graph on 3 vertices and any number of isolated vertices. If you mean a graph that is (isomorphic to) a cycle, then the answer is n. If you are really asking the maximum number of edges, then that would be the triangle numbers such as n (n-1) /2.
Prove that every tree with two or more vertices is bichromatic?
Prove that the maximum vertex connectivity one can achieve with a graph G on n. 01. Define a bipartite graph. Prove that a graph is bipartite if and only if it contains no circuit of odd lengths. Define a cut-vertex. Prove that every connected graph with three or more vertices has at least two vertices that are not cut vertices. Prove that a connected planar graph with n vertices and e edges has e - n + 2 regions. 02. 03. 04. Define Euler graph. Prove that a connected graph G is an Euler graph if and only if all vertices of G are of even degree. Prove that every tree with two or more vertices is 2-chromatic. 05. 06. 07. Draw the two Kuratowski's graphs and state the properties common to these graphs. Define a Tree and prove that there is a unique path between every pair of vertices in a tree. If B is a circuit matrix of a connected graph G with e edge arid n vertices, prove that rank of B=e-n+1. 08. 09.
How many subgraphs with at least one vertex does a complete graph of 3 vertices k3 have?
one vertex: 3 two vertices: 6 three vertices: 8 total 17
How many edges are there in a graph with 7 vertices each with degree 2?
There are 7 edges.
The minimum number of edges in a connected cyclic graph on n vertices is?
n-1
How can you design an algorithm to check if a given graph is connected?
Use a simple DFS/BFS traversal. If you have gone through all nodes, the graph is connected.
In depth first traversal of a graph G with n vertices k edges are marked as tree edges the no of connected components in G is?
n-k-1
Define walk path and connected graph in an algorithm?
A "walk" is a sequence of alternating vertices and edges, starting with a vertex and ending with a vertex with any number of revisiting vertices and retracing of edges. If a walk has the restriction of no repetition of vertices and no edge is retraced it is called a "path". If there is a walk to every vertex from any other vertex of the graph then it is called a "connected" graph.
What is difference between resource allocation graph and resource allocation graph algorithm?
The graph is the the actual picture that shows the resource allocation; the algorithm is the method used to produce that graph.
Difference between a directed graph and an undirected graph in a computer program?
In an undirected graph, an edge is an unordered pair of vertices. In a directed graph, an edge is an ordered pair of vertices. The ordering of the vertices implies a direction to the edge, that is that it is traversable in one direction only.
What is subgraph in given graph?
If all the vertices and edges of a graph A are in graph B then graph A is a sub graph of B.
How can i use a graph to find the number of vertices in a octagonal pyramid?
The number of vertices in an octagonal pyramid is 9, irrespective of any graph.
Which is the best shortest path algorithm?
dijkstra's algorithm (note* there are different kinds of dijkstra's implementation) and growth graph algorithm
An algorithm to find whether a directed graph is connected or not?
You can use a The Depth-First Search algorithm.
What is the complexity of Floyd warshall algorithm?
The Floyd-Warshall algorithm is a classic example of dynamic programming used to find the shortest paths between all pairs of vertices in a weighted graph. It's a powerful algorithm that works for both directed and undirected graphs, and handles negative weights as well. The algorithm operates in a systematic manner, progressively building up the solution by considering intermediate vertices between each pair of vertices, and determining if a shorter path can be found by going through that intermediate vertex. The core of the Floyd-Warshall algorithm involves three nested loops. The outer loop iterates through each vertex in the graph, treating it as an intermediate vertex. The two inner loops iterate through all pairs of vertices, checking and updating the shortest path between them if a shorter path is found through the intermediate vertex. Due to this triple nested loop structure, the time complexity of the Floyd-Warshall algorithm is often expressed as O(n3) where n is the number of vertices in the graph. While the time complexity might seem high, the Floyd-Warshall algorithm's ability to solve the all-pairs shortest path problem in a straightforward and understandable manner makes it a valuable tool in the realm of graph theory and network analysis. The space complexity of the algorithm is O(n2) as it requires a two-dimensional matrix to store the shortest path distances between all pairs of vertices. The matrix used by the Floyd-Warshall algorithm is initialized with the direct distances between vertices, and is progressively updated through the algorithm's iterations. Each cell in the matrix ultimately contains the shortest distance between the corresponding pair of vertices. In practical scenarios, the Floyd-Warshall algorithm can be used in various domains including routing protocols in networking, travel itinerary planning, and in many applications where optimizing routes through networks is crucial. Despite its cubic time complexity, the Floyd-Warshall algorithm's ability to handle negative weights and its straightforward implementation makes it a popular choice for the all-pairs shortest path problem, especially when the graph has a relatively small number of vertices, or when a precise and comprehensive solution is required over performance. In conclusion, the Floyd-Warshall algorithm is a compelling, albeit computationally intensive, method to solve the all-pairs shortest path problem. Its cubic time complexity might be a deterrent for extremely large graphs, yet its robustness and simplicity keep it relevant in many practical situations where understanding and optimizing network pathways are essential.
What is a drawing graph?
A drawing of a graph or network diagram is a pictorial representation of the vertices and edges of a graph. This drawing should not be confused with the graph itself: very different layouts can correspond to the same graph. In the abstract, all that matters is which pairs of vertices are connected by edges.
What is an adjacency matrix?
An adjacency matrix is a matrix showing which vertices of a graph are adjacent to which other vertices.
