Give an example of two non-isomorphic maximal planar graphs of the same order.

Solutions

Expert Solution

Given that,

We consider the graphs on 10 vertices: and , respectively. The edges of are given below:

Now, the edges for are as follows:

These are planar graphs of order 10, (see diagrams) having 24 edges each; they are maximal since addition of an extra edge to either would make it non-planar. However, they are non-isomorphic since the maximal degrees differ: we have

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Determine all maximal planar graphs G of order 3 or more such that the number of...

Determine all maximal planar graphs G of order 3 or more such that the number of regions in a planar embedding of G equals its order.

How many non-isomorphic 5-vertex connected planar graphs are there? Use Sage to produce / depict them....

How many non-isomorphic 5-vertex connected planar graphs are there? Use Sage to produce / depict them. Include your Sage code. A number alone will receive no credit.

How many colors are needed to color a planar graphs? Give a proof that each planar...

How many colors are needed to color a planar graphs? Give a proof that each planar graph can be colored with at most 6 colors. (Hint:induction. Use the fact that each planar graph has a vertex of degree no more than 5.) Please include all explanantion and steps. Also draw the diagram too so i understand it better. Thanks!

(i) There are two non-isomorphic groups of order 4: C4 and C2xC2. Let C3 be a...

(i) There are two non-isomorphic groups of order 4: C4 and C2xC2. Let C3 be a cyclic group of order 3. For each group G of order 4, determine all possible homomorphisms f an element of Hom(C3, Aut(G)). (ii) For C3 and each G of order 4 as above, determine all possible homomorphisms phi an element of Hom(G, Aut(C3)).

give a four-point example P that has both maximal point not on the convex hull and...

give a four-point example P that has both maximal point not on the convex hull and a convex hull point is not maximal

Prove that every complete lattice has a unique maximal element. (ii) Give an example of an...

Prove that every complete lattice has a unique maximal element. (ii) Give an example of an infinite chain complete poset with no unique maximal element. (iii) Prove that any closed interval on R ([a, b]) with the usual order (≤) is a complete lattice (you may assume the properties of R that you assume in Calculus class). (iv) Say that a poset is almost chain complete if every nonempty chain has an l.u.b. Give an example of an almost chain...

Question