- finite undirected gragh
∑deg(v) = 2|E|
In a k-ary tree where every node has either 0 or k children, following property is always true.
L = (k - 1)*I + 1 Where L = Number of leaf nodes I = Number of internal nodes
case: root is leaf/internal node
Sum of all degrees = 2 * (Sum of Edges) L + (I-1)*(k+1) + k = 2 * (L + I - 1) L + k*I - k + I -1 + k = 2*L + 2I - 2 L + K*I + I - 1 = 2*L + 2*I - 2 K*I + 1 - I = L
(K-1)*I + 1 = L
https://www.geeksforgeeks.org/handshaking-lemma-and-interesting-tree-properties/