The neighborhood of a vertex in a graph consists of the vertex itself, together with all...

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Advance Math

The neighborhood of a vertex in a graph consists of the vertexitself, together with all vertices that are connected to it by anedge. Each graph has a variable xi associated with the i-th vertex,and the vertex has a known value that is equal to the sum of thevariables for all neighborhood vertices. Start with a graph with 5vertices forming a pentagon, with edges joining vertices 1 and 2, 2and 3, 3 and 4, 4 and 5, and 5 and 1. Then draw an edge joiningvertices 2 and 4, and an edge joining vertices 2 and 5. The knownvalues at vertices 1 through 5 are, respectively, 2, 1, ?1, 3, and5.
(a) Find the augmented matrix for the system of equationssatisfied by x₁, x₂, x₃,x₄, x_5.

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Given the graphwith 5vertices say Also given that the vertices are connected by the edgesAlso the known values at vertices are respectivelyBy the given definition See Answer

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