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  3. the neighborhood of a vertex in a graph consists o

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, x5.

Answer & Explanation Solved by verified expert
3.9 Ratings (666 Votes)
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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