Is there a graph with 5 vertices with the vertex degree 4 4 3 2 2 respectively?
if yes, please show an example,
if not, please proove it
in an undirected graph, total number of degrees of all vertices must be even. because each edge gives a total degree of 2(degree of 1 at each vertex) in this graph, sum of all degrees is 4+4+3+2+2 = 15 which is odd. this is not possible for a valid graph. so, there is no such graph.
Is there a graph with 5 vertices with the vertex degree 4 4 3 2 2...
Recall the definition of the degree of a vertex in a graph. a) Suppose a graph has 7 vertices, each of degree 2 or 3. Is the graph necessarily connected ? b) Now the graph has 7 vertices, each degree 3 or 4. Is it necessarily connected? My professor gave an example in class. He said triangle and a square are graph which are not connected yet each vertex has degree 2. (Paul Zeitz, The Art and Craft of Problem...
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Discrete Mathematics 6: A: Draw a graph with 5 vertices and the requisite number of edges to show that if four of the vertices have degree 2, it would be impossible for the 5 vertex to have degree 1. Repetition of edges is not permitted. (There may not be two different bridges connecting the same pair of vertices.) B: Draw a graph with 4 vertices and determine the largest number of edges the graph can have, assuming repetition of edges...
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