Calculate the number of spanning trees of the graph with the following adjacency matrix: 0 1 0 1 1 10 100 0 1 0 1 0 1 0 1 0 1 100 10,

(5) The definition of weighted graph is such that every edge has positive weight. If the def- inition was changed to permit negative (or zero) weights, would Kruskal's and Dijkstra's algorithms continue to work? Give a proof or counterexample in each case.

Choose the project network for the following project. The project is completed when activities E, F and G are complete. Activity Immediate Predecessor Start Start B A D A B C -A, D E O D A E B, D Finish Fanush F B, D (lv) G C (H) Start Start B B E E E 0 Firush Finish

Consider the relation on A = {a, b, c, d, e} given by R = {(a,b), (b,c),(b,d), (b,e),(d,e)}

(4) Assume that a website www.funwithmath1600.ag has three pages: Page A: KingAlgebra Page B: Learn1600andWin • Page C: Linear AlgbraIsEverywhere Each page has some links to the other pages of this website and no pages links to any page outside this website. Page A has three links to page B and only one link to page C. • Page B has three links to page A and two links to page C. • Page C has one link to page A and two links to page B. A student decides to explore this website starting from page A. Since reading content is always a boring task (is it?!) they decide to choose one of the links in page A with equal probability and click on the link to see the next page. As a result, on the next step, they will end up on page B with probability 3/4 and on the page C with probability 1/4. This process is then continued by the student with the same rule: Go the next page by clicking, with equal probability, on one of the existing links that are on the present page. (Use only fractions in your…