Graph Theory

Graphs and digraphs by Chartrand G., Lesniak L., Zhang P.

By Chartrand G., Lesniak L., Zhang P.

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As expected, G1 G2 ∼ = G2 G1 for all graphs G1 and G2 . G1 : G2 : .. ..... ... ...... ........ .. ...... ..... ............ ...... ...... .. ... ..... ....... ... .... . . ... ..... ......... ..... ... ... (a) ....... .. ..... . . .... ......... ..... . ... .... .... ..... ..... . . .... ...... ..... ..... ...... ......... ..... ..... ..... . . ............ ..... ..... ....... .... .. ... ..... ..... ..... . . ............ ...... .............

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?

An electronics company keeps on hand wire segments of a fixed length and of different colors for various purposes. Each wire is either colored blue (b), green (g), purple (p), red (r), silver (s), white (w) or yellow (y). The company has many wire segments of each color. All of the wire segments have been randomly stored in a large barrel. Eight handfuls of wires are removed from the barrel and each collection of wires is placed in a box. The boxes are denoted by Bi (1 ≤ i ≤ 8). The colors of the wire segments in each box are: B1 = {b, r} B5 = {g} B2 = {p, r, s, w} B6 = {b, g, y} B3 = {p, w, y} B7 = {g, p, s, w, y} B4 = {g, r, y} B8 = {s, w, y}.

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