Isomorphic Graphs Have the Same Degree Sequence Graph Theory

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We prove that isomorphic graphs have the same degree sequence. This isn't too surprising since graph isomorphisms preserve adjacency and non-adjacency of vertices by definition. We'll prove it by taking an arbitrary vertex from our graph G, and show it has the same degree as its image under the isomorphism in the isomorphic graph H. This proves that every vertex of G has the same degree as its corresponding vertex in H, and remember isomorphisms are bijections, so this covers all vertices of G as well as those of H. Since the degree sequence of a graph is just the non-increasing list of the vertex degrees, this means isomorphic graphs (G and H) have the same degree sequence. • Isomorphic Graphs: • What are Isomorphic Graphs? | Graph I... • Degree Sequence of a Graph: • Degree Sequence of a Graph | Graph Th... • ★DONATE★ • ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: / wrathofmathlessons • ◆ Donate on PayPal: https://www.paypal.me/wrathofmath • Thanks to Robert Rennie and Barbara Sharrock for their generous support on Patreon! • Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: https://crayonangel.bandcamp.com/ • Follow Wrath of Math on... • ● Instagram: / wrathofmathedu • ● Facebook: / wrathofmath • ● Twitter: / wrathofmathedu • My Music Channel: / @emery3050

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