Question

Graph Theory Let v be a vertex of a non trivial graph G. prove that if...

Graph Theory

Let v be a vertex of a non trivial graph G. prove that if G is connected, then v has a neighbor in every component of G-v.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let G be a graph or order n with independence number α(G) = 2. (a) Prove...
Let G be a graph or order n with independence number α(G) = 2. (a) Prove that if G is disconnected, then G contains K⌈ n/2 ⌉ as a subgraph. (b) Prove that if G is connected, then G contains a path (u, v, w) such that uw /∈ E(G) and every vertex in G − {u, v, w} is adjacent to either u or w (or both).
Let G be a graph with vertex set V. Define a relation R from V to...
Let G be a graph with vertex set V. Define a relation R from V to itself as follows: vertex u has this relation R with vertex v, u R v, if there is a path in G from u to v. Prove that this relation is an equivalence relation. Write your proof with complete sentences line by line in a logical order.  If you can, you may write your answer to this question directly in the space provided.Your presentation counts.
Let G be an n-vertex graph with n ≥ 2 and δ(G) ≥ (n-1)/2. Prove that...
Let G be an n-vertex graph with n ≥ 2 and δ(G) ≥ (n-1)/2. Prove that G is connected and that the diameter of G is at most two.
let G be a connected graph such that the graph formed by removing vertex x from...
let G be a connected graph such that the graph formed by removing vertex x from G is disconnected for all but exactly 2 vertices of G. Prove that G must be a path.
Let ? be a connected graph with at least one edge. (a) Prove that each vertex...
Let ? be a connected graph with at least one edge. (a) Prove that each vertex of ? is saturated by some maximum matching in ?. (b) Prove or disprove the following: Every edge of ? is in some maximum matching of ?.
Let G=(V,E) be a connected graph with |V|≥2 Prove that ∀e∈E the graph G∖e=(V,E∖{e}) is disconnected,...
Let G=(V,E) be a connected graph with |V|≥2 Prove that ∀e∈E the graph G∖e=(V,E∖{e}) is disconnected, then G is a tree.
Prove or disapprove each of the following: (a) Every disconnected graph has an isolated vertex. (b)...
Prove or disapprove each of the following: (a) Every disconnected graph has an isolated vertex. (b) A graph is connected if and only if some vertex is connected to all other vertices. (c) If G is a simple, connected, Eulerian graph, with edges e, f that are incident to a common vertex, then G has an Eulerian circuit in which e and f appear consequently.
Graph Theory Prove that if G is a graph with x(G-v-w)=x(G)-2 for every pair of vertices...
Graph Theory Prove that if G is a graph with x(G-v-w)=x(G)-2 for every pair of vertices v and w in G, then G is complete. Hint: assume G is not complete.
Let G be a graph where every vertex has odd degree, and G has a perfect...
Let G be a graph where every vertex has odd degree, and G has a perfect matching. Prove that if M is a perfect matching of G, then every bridge of G is in M. The Proof for this question already on Chegg is wrong
Let G be a graph whose vertex set is a set V = {p1, p2, p3,...
Let G be a graph whose vertex set is a set V = {p1, p2, p3, . . . , p6} of six people. Prove that there exist three people who are all friends with each other, or three people none of whom are friends with each other.