3) The graph k-coloring problem is stated as follows: Given an undirected graph G= (V,E) with N vertices and M edges and an integer k. Assign to each vertex v in V a color c(v) such that 1

Extracted text: 3) The graph k-coloring problem is stated as follows: Given an undirected graph G= (V,E) with N vertices and M edges and an integer k. Assign to each vertex v in V a color c(v) such that 1< c(v)="" for="" every="" edge="" (u,="" v)="" in="" e.="" in="" other="" words="" you="" want="" to="" color="" each="" vertex="" with="" one="" of="" the="" k="" colors="" you="" have="" and="" no="" two="" adjacent="" vertices="" can="" have="" the="" same="" color.="" (2="" marks)="" for="" example,="" the="" following="" graph="" can="" be="" 3-colored="" using="" the="" following="" color="" assignments:="" a="1,b=2,c%3D1,d%32,e3D3,f32,g=3" a---b---c---g="" d="" f="" formulate="" the="" graph="" k-coloring="" problem="" as="" an="" evolutionary="" optimization.="" you="" may="" use="" a="" vector="" of="" integer="" representation,="" or="" any="" representation="" that="" you="" think="" is="" more="" appropriate.="" you="" should="" specify:="" a="" representation.="" •="" a="" fitness="" function.="" give="" 3="" examples="" of="" individuals="" and="" their="" fitness="" values="" if="" you="" are="" solving="" the="" above="" example.="" •="" a="" set="" of="" mutation="" and/or="" crossover="" and/or="" repair="" operators.="" intelligent="" operators="" that="" are="" suitable="" for="" this="" particular="" domain="" will="" earn="" more="" credit.="" •="" a="" termination="" criterion="" for="" the="" evolutionary="" optimization="" which="" insures="" that="" you="" terminate="" with="" a="" valid="" solution="" to="" the="" graph="" k-coloring="" problem="" if="" possible="" without="" running="">