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- Prove that If a connected planar simple graph has e edges and v vertices with v ≥ 3 and no circuits of length three, then e ≤ 2v − 4. (Show work)Sketch a diagram such that the vertices of △ABC lie respectively on the sides of △XYZ so that AX, BY, CZ are concurrent.Prove that a complete bipartile graph Ks,s has (s−1)!s!/2 Hamiltonian walks for s >1
- Prove that the digraph obtained from Cay({(1, 0), (0, 1)}:Z4 ⊕ Z7)by deleting the vertex (0, 0) has a Hamiltonian circuit.prove that the maximum girth of a generalized Coxeter graph is 12, no matter what its parameters are.If countries in the Southeast region are consisting of archipelagos then other foreign countries cannot invade it. Indonesia is located in the Southeast region. With that other foreign countries cannot invade it. What is the euler diagram for this problem?
- Represent the polyhedron defined by x1+x2>=1 with a minimal set of generators. Thanks !(Show your work) compute the girth of all generalized Coxeter graphs with parameter Pn,u,v where n is less or equal to12I need proof this thm ASAP I vll upvote for u If u prove within 30 minutes Prove that if there exists at most one path between any two vertices of a simple graph G, then G is a forest and conversely.
- Suppose S is the unit cube in the first octant of uvw-space withone vertex at the origin. What is the image of the transformationT: x = u/2, y = v/2, z = w/2?Prove that Two lattice points (a,b) and (m,n) are mutually visible if and only if a−m and b−n are relatively primeAssume a directed acyclic graph is encoded as a relation R. Give a concise proposition stating that R is irreflexive (i.e., that no nodes have edges to themselves).