Let n ≥ 3. Show that if G is a graph with the same chromatic polynomial...

Let n ≥ 3. Show that if G is a graph with the same chromatic polynomial as Cn, then G is isomorphic to Cn. (Hint: Use induction. What kind of graph must G − e be for any edge e? Why?)

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Colby Messinger answered 1 year ago

Let G be a simple planar graph with no triangles. (a) Show that G has a...

Let G be a simple planar graph with no triangles. (a) Show that G has a vertex of degree at most 3. (The proof was sketched in the lectures, but you must write all the details, and you may not just quote the result.) (b) Use this to prove, by induction on the number of vertices, that G is 4-colourable.

Let G = R\{0} and N = (0,∞). Show that G/N is isomorphic to the multiplicative...

Let G = R\{0} and N = (0,∞). Show that G/N is isomorphic to the multiplicative group {1, −1}.

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Let Q:= {1,2,...,q}. Let G be a graph with the elements of Q^n as vertices and an edge between (a1,a2,...,an) and (b1,b2,...bn) if and only if ai is not equal to bi for exactly one value of i. Show that G is Hamiltonian.

Let G be a simple undirected graph with n vertices where n is an even number....

Let G be a simple undirected graph with n vertices where n is an even number. Prove that G contains a triangle if it has at least (n^2 / 4) + 1 edges using mathematical induction.

let G be a simple graph. show that the relation R on the set of vertices...

let G be a simple graph. show that the relation R on the set of vertices of G such that URV if and only if there is an edge associated with (u,v) is a symmetric irreflexive relation on G

A maximal plane graph is a plane graph G = (V, E) with n ≥ 3...

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Let n ≥ 3. Show that if G is a graph with the same chromatic polynomial...

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