Counting Edges Examples

Graph Theory · Axiom Academy

EXAMPLE Counting Edges Examples Master edge counting techniques through worked examples Problem: Find the number of edges Excellent work! You've mastered counting edges in graphs. Here's what we learned: Handshaking Lemma: The sum of all vertex degrees equals twice the number of edges: Σdeg(v) = 2|E| Degree Sequences: For a sequence to be graphical, the sum of degrees must be even (since each edge contributes 2 to the total) Complete Graphs: A complete graph K n has exactly n(n-1)/2 edges, connecting every pair of vertices Bipartite Graphs: The maximum edges in K m,n is m × n , connecting all vertices between the two sets Verification Strategy: Always check if your degree sum is even and if the degree sequence satisfies the necessary conditions These formulas and techniques are fundamental to graph theory. Practice applying them to different graph types to build intuition!

This is the written version of the interactive lesson above. See the full Graph Theory course.