3-restricted connectivity of graphs with given girth by Guo L.-T.

By Guo L.-T.

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27: Two graphs with the same degree sequence edges in F are added to F such that the four edges involved are incident with the same four vertices. The Havel-Hakimi Theorem Let H be a graph containing four distinct vertices u, v, w and x such that uv, wx ∈ E(H) and uw, vx ∈ / E(G). 28, where a dashed line means no edge). This produces a new graph G having the same degree sequence as H. u u v ... ...... . . . . ..... .... ...... .... . . . ...... w x v ...... ..... . . . . .. ...........

An ) or a1 a2 · · · an such that ai is 0 or 1 for 1 ≤ i ≤ n (commonly called n-bit strings), such that two vertices are adjacent if and only if the corresponding ordered n-tuples differ at precisely one coordinate. The graph Qn is an nregular graph of order 2n . 23, where their vertices are labeled by n-bit strings. The graphs Qn are often called hypercubes. 110 10 11 ............ ... ............. ............ .............. 1 00 01 0 . ... Q1 : .............. ............ .... . ...

32: The graphs in Exercise 2 3. Let s : 2, 2, 2, 2, 2, 2, 2, 2, 2 and let Gs be the set of all graphs with degree sequence s. Let G be a graph with V (G) = Gs where two vertices F and H in G are adjacent if F can be transformed into H by a single 2-switch. Which familiar graph is G isomorphic to? 4. 2. DEGREE SEQUENCES (2) two vertices F and H of G are adjacent if F can be transformed into H by a single 2-switch and (3) G contains a triangle.

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