8 mat3707201 10 for each of the following pairs of

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MAT3707/20110. For each of the following pairs of graphs determine whether they are isomorphic or not. If they are,give a vertex correspondence. If they are not, give a reason why.(a)83741265hcgdabfe(5)
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11. Find a Hamilton path in the graph below and prove that no Hamilton circuit exists.abcnopedfgjlkmhi(6)
12. Use the circle-chord method to determine whether the following graph is planar. If it is, give a planardrawing. It if is not, find aK3,3- orK5-configuration.bacjikfegdh(8)
(See example 4, section 1.4 (Tucker)andStudy Guide p.15 & 16).We use the Hamilton circuitabefghckjida. By inside-outside symmetry we choose the edgeafto bedrawn inside. Then the edgebchas to be drawn outside. Now the edgedecannot be drawn inside oroutside. (Find edges in such a way that the previous choices force the next edge to be drawn inonlyone possible way.)Hence the graph is not planar:becghjiafkdThe following is aK3,3configuration of the graph,aecfdbkighj10
MAT3707/20113. Determine the chromatic number of each of the following graphs. Give a minimal colouring and aproof that a smaller number of colours cannot be used.(a)bacdfeg(5)
(b)bacdfeghnmopjikl(5)
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(c)abcdefghij(5)

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Term
Spring
Professor
NoProfessor
Tags
Graph Theory, Tucker, Planar graph

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