Why a complete graph has $\\frac{n(n-1)}{2}$ edges?
$\frac{n(n-1)}{2} = \binom{n}{2}$ is the number of ways to choose 2 unordered items from n distinct items. In your case, you actually want to count how many unordered pair of vertices …
How many Hamiltonian cycles are there in a complete graph
I can see why you would think that. For n=5 (say a,b,c,d,e) there are in fact n! unique permutations of those letters.
Eigenvalues of a Complete graph - Mathematics Stack Exchange
2015年9月5日 · To make matters worse I have just noted that the determinant of the adjacency matrix of a complete graph with n vectors is $(-1)^{n-1}(n-1)$ which also mean my belief is …
Subgraphs of Complete graphs - Mathematics Stack Exchange
You need to consider two thinks, the first number of edges in a graph not addressed is given by this equation Combination(n,2) becuase you must combine all the nodes in couples, In …
What is the degree of a vertex in the complete graph $K_n$?
2019年2月23日 · Because every two points are connected in a complete graph, each individual point is connected with every other point in the group of n points. There is a connection …
What is the difference between a simple graph and a complete …
2014年4月16日 · Every complete graph is also a simple graph. However, between any two distinct vertices of a complete graph, there is always exactly one edge; between any two distinct …
Standard notation for the complete graph with self-loops?
2018年6月22日 · I'm in with Mike, standard notation is rare in graph theory. People can't even agree if "graph" without additional information refers to "simple graph" (no loops and multiple …
Finding the number of Spanning Trees of a Graph $G$
$\begingroup$ A complete graph is a graph where every pair of vertices is joined by an edge, thus the number of edges in a complete graph is $\frac{n(n-1)}{2}$. This gives, that the number of …
a regular graph has 15 edges, how many vertices does it have?
2015年10月24日 · It's not true that in a regular graph, the degree is $|V| - 1$. The degree can be 1 (a bunch of isolated edges) or 2 (any cycle) etc. In a complete graph, the degree of each …
Number of cycles in complete graph - Mathematics Stack Exchange
2015年7月17日 · In a complete graph, every choice of n vertices is a cycle, so if the graph has k vertices, then there is $\sum_{n=3}^{k} {k \choose n}$, which is equal to $ \dfrac{-k^2}{2} …