In a simple undirected graph H the sum of vertex degrees is 60. What is the...

In a simple undirected graph H the sum of vertex degrees is 60. What is the smallest possible number of vertices in this graph? What is the largest possible number of vertices in the graph?

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Colby Messinger answered 2 years ago

Given an undirected graph G=(V, E) with weights and a vertex , we ask for a...

Given an undirected graph G=(V, E) with weights and a vertex , we ask for a minimum weight spanning tree in G where is not a leaf (a leaf node has degree one). Can you solve this problem in polynomial time? Please write the proof.

(a) What is the maximum degree of a vertex in a simple graph with n vertices?...

(a) What is the maximum degree of a vertex in a simple graph with n vertices? (b) What is the maximum number of edges in a simple graph of n vertices? (c) Given a natural number n, does there exist a simple graph with n vertices and the maximum number of edges?

Prove or disprove: If G = (V; E) is an undirected graph where every vertex has...

Prove or disprove: If G = (V; E) is an undirected graph where every vertex has degree at least 4 and u is in V , then there are at least 64 distinct paths in G that start at u.

A symmetrical wedge having a total vertex angle of 60 degrees is traveling at a Mach...

A symmetrical wedge having a total vertex angle of 60 degrees is traveling at a Mach number of 3 at an altitude of 15 km. What are the static values of the pressure, density, and temperature downstream of the shock, and what are the stagnation values of those quantities? What is the percentage loss of the stagnation pressure across the shock wave?

Let G be a simple undirected graph with n vertices where n is an even number....

Let G be a simple undirected graph with n vertices where n is an even number. Prove that G contains a triangle if it has at least (n^2 / 4) + 1 edges using mathematical induction.

ive an example of a simple, undirected graph that has a single source shortestpath tree which...

ive an example of a simple, undirected graph that has a single source shortestpath tree which breadth-first search will not return for any ordering of its vertices.Your answer must (a) Specify the graphG= (V, E)by specifying V and E. (b) Specify the single source shortest path treeT= (V, ET) by specifying E T and also specifying the roots∈V. (c) and include a clear explanation of why the breadth-first search algorithm we discussed in class will never produce T for any...

give an example of a simple, undirected, weighted graph such that breadth-firstsearch outputs a search-tree that...

give an example of a simple, undirected, weighted graph such that breadth-firstsearch outputs a search-tree that is not a single source shortest path tree. Youranswer must (a) Specify the graphG= (V, E)by specifyingVandE. (b) Specify the weight functionw. (c) Specify an ordering of the vertices and the search-tree output by breadth-first search assuming the specified graph and ordering. (d) Specify a valid single-source shortest path treeT= (V, ET)by specifyingETand its root, the first vertex in your specified ordering. (e) Include...

Let Kn denote the simple graph on n vertices. (a) Let v be some vertex of...

Let Kn denote the simple graph on n vertices. (a) Let v be some vertex of Kn and consider K n − v, the graph obtained by deleting v. Prove that K n − v is isomorphic to K n−1 . (b) Use mathematical induction on n to prove the following statement: K n , the complete graph on n vertices, has n(n-1)/2 edges

The neighborhood of a vertex in a graph consists of the vertex itself, together with all...

The neighborhood of a vertex in a graph consists of the vertex itself, together with all vertices that are connected to it by an edge. Each graph has a variable xi associated with the i-th vertex, and the vertex has a known value that is equal to the sum of the variables for all neighborhood vertices. Start with a graph with 5 vertices forming a pentagon, with edges joining vertices 1 and 2, 2 and 3, 3 and 4, 4...

Which graph search method will be better for finding a cycle in an undirected graph: a...

Which graph search method will be better for finding a cycle in an undirected graph: a BTS or a DFS? In detail, describe (create) an algorithm for finding a cycle in any undirected graph, explaining why the algorithm assures to find a cycle if there exists one.

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