Question

what is the maximum degree of any vertex in a single graph with n vertices can you please explain with figure​

Answer 1

Answer:

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Step-by-step explanation:

If you mean a simple graph, with at most one edge connecting two vertices, then the maximum degree is  n−1.

A complete graph with n  vertices is a simple graph where every vertex has degree  n−1, that is, each vertex is (directly) connected with every other vertex with an edge. In this case, the number of edges is n(n−1)2=(n2).

:

n(n-1)/2

every vertex connected to every other vertex

ex {a,b,c,d,e}

a connected to b a connected to c = 4 a connected to d a connected to e

b connected to c b connected to d = 3 b connected to e

c connected to d =2 c connected to e

d connected to e =1

This is an arithmetic progression with a common difference=1 and base term as 1.

there is a nice formula to calculate its sum as n(n-1)/2

hence apply the formula