A graph thát iš connected and has no circuits is called a/an For such a graph, • every edge is a/an • if there are n vertices, there must be edges

Q: Construct a graph with vertices P, Q, R, S, T, U, V that has an Euler path, the degree of R is 1 and…

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Q: 5. For a chess piece Q, the Q-graph is the graph whose vertices are the squares of the chess board…

A: The least amount of colours required to colour all the vertex edges of a graph so that no two…

Q: construct a graph with vertices Q,R,S,T,U,V,W that has an Euler path and the degree of U is 1 and…

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Q: A set S of vertices is an independent set if there are no edges between any two vertices in S (e.g.,…

A: The statement is not true.

Q: A connected graph has 80 even vertices and two odd vertices Determine whether the graph has an Euler…

A: Using Euler's theorem,  A graph has an Euler circuit if and only if degree of each vertex is even.…

Q: Illustrate the key ideas in the proof that a connected graph has an Euler circuit if and only if…

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Q: Suppose you colored edges of a graph either red or blue (not requiring that adjacent edges be…

A: According to the given information, Let the edges of the graph be coloured with red or blue. It is…

Q: "If G has a walk that uses all the edges, then G is connected." I know that this statement is false…

A: If G has a walk that uses all the edges, then G is connected Clearly this statement is false For…

Q: find the number of the isomorphism classes of graphs with 5 vertices and 6 edges which have (i)…

A: Given the a graphs with 5 vertices and 6 edges. We have to find the number of the isomorphism…

Q: Prove that If a connected planar simple graph has e edges and v vertices with v ≥ 3 and no circuits…

A: A bipartite graph is a simple graph whose vertices can be partitioned into two sets V1​ and V2​ such…

Q: Show a Hesse diagram with 5 nodes {1, 2, 3, 4, 5} and 4 edges that has exactly three topological…

A: Given nodes are 1,2,3,4,5 with 4 edges. We know that a topological sorting for a directed acyclic…

Q: What is the number of isomorphism classes of graphs with 6 vertices and 3 edges

A: It is known that sum of degree in a graph must be even because sum of degrees is  twice the edges.…

Q: Use Euler's theorem to determine whether the graph has an Euler path (but not an Euler circuit),…

A: Given that, the graph has 102 even vertices and no odd vertices.

Q: 2. Prove that any graph has at least two vertices with the same degree. A complete bipartite graph…

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Q: Construct a simple graph with vertices F, G, H, I,J that has an Euler circuit and the degree of F is…

A: A graph is said to be simple if it has no loops and parallel edges. Degree of a vertex of a graph is…

Q: Prove that if a graph on n vertices is connected, and has n-1 edges, it must be acyclic.

A: A graph G is said to be a connected graph, if there is a path between any two vertices in that…

Q: K3 Euler path: Euler circuit: Hamilton path: Hamilton circuit:

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