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What is cyclomatic number of a graph is called?
cyclomatic number of a graph is e.n+1 where e is number of edge of graph and n is number of node in graoh g
Prove that a graph G is connected and only if it has a spanning tree?
Proving this is simple. First, you prove that G has a spanning tree, it is connected, which is pretty obvious - a spanning tree itself is already a connected graph on the vertex set V(G), thus G which contains it as a spanning sub graph is obviously also connected. Second, you prove that if G is connected, it has a spanning tree. If G is a tree itself, then it must "contain" a spanning tree. If G is connected and not a tree, then it must have at least one cycle. I don't know if you know this or not, but there is a theorem stating that an edge is a cut-edge if and only if it is on no cycle (a cut-edge is an edge such that if you take it out, the graph becomes disconnected). Thus, you can just keep taking out edges from cycles in G until all that is left are cut-gees. Since you did not take out any cut-edges, the graph is still connected; since all that is left are cut-edges, there are no cycles. A connected graph with no cycles is a tree. Thus, G contains a spanning tree. Therefore, a graph G is connected if and only if it has a spanning tree!
How do you graph fx-x-1 3 gx-x-2 and hx -3x-1?
graph G(x)=[x]-1
What is a divisor graph?
Let S be a finite, non-empty set of positive integers. The divisor graph G(S) of S has S as its vertex set, and two distinct vertices i and j are adjacent if and only if either idivides j or j divides i. Let G be a simple graph. Then G is called a divisor graph if G is isomorphic to G(S) for some non-empty, finite set S of positive integers.REFERENCE :S. Ganesan, D. Uthayakumar, Corona of Bipartite Graphs with Divisor GRaphs Produce New Divosor Graphs,Bulletin of Kerala Mathematics AssociationVol.9, No.1, (2012, June) 219-226
Why does it make sense that by graphing two rational functions on the same graph be the same as if you were to add them first then graph?
It is not. If f(x) = ax2 and g(x) = -ax2 then the separate graphs will be two quadratic curves, f being "happy" and g being "sad". But f(x) + g(x) = 0 for all x and so is the x axis, not a quadratic.
