*If G is k-regular and connected but there is a vertex v such that Gv is disconnected, then prove that x'(G) = k +1.
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- If (an) has limit −1 and (bn) tends to infinity, does it follow that only finitely many terms of (anbn) are positive?Prove : for r belongs to Z+, every r connected graph on an even number of vertices with no induced subgraph isomorphic to k1,r+1 has a 1-factor. Show that this is not true if you replace r connected by r edge connected(Show your work) prove that the maximum girth of a generalized Coxeter graph is 12, no matter what its parameters are.
- Find the maximal value for delta>0 such that, for all x, if 2<x<2+delta , then square root of x - 2 < 0.3.prove that the maximum girth of a generalized Coxeter graph is 12, no matter what its parameters are.b) If (an) has limit−1 and (bn) tends to infinity, does it follow that only finitely many terms of (an bn) are positive?
- There's a connection between the Existence and Uniqueness Theorem for constant-coefficient, linear, homogeneous IVP's and linear algebra.(Show your work) compute the girth of all generalized Coxeter graphs with parameter Pn,u,v where n is less or equal to12Prove that limit x goes to 2 x^(3)+3 = 11 (Using epsilon-delta proof)