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Discrete Structures Assignment # 3 Name: Zehra Ahmad Roll no: 24P-3045 Class: SE-3A . 3 h ‘ d k Fig (a) Chromotic Number of Crvophs Gi eal mee a a tg hig k Color Red Ble => 40, CN=2 Foyt) : < - A Qroph has 1000 vertices & 4 ealge vertices - So only 4 paive of Cpe is connected yyheyeas thee ove 998 isdoted vertices. . » The isolated vertices can be: of andy coli and we need ony Q colors for each eonnected verbir- - Hence the CN is Q- Part (6) “A cwouloy goph hase 199 chovdo porolel to eachesther. + Each of the 199 parallel chords har 2 end points. > 199K 2 = 399 vertices. » These 298 points divide the circle j edges and civle into 398 boundoy 199 chord edges. > 3984499 = 547 EAL edges. Question: 2 Poyt :O * Ke > 6 vertices Paxt:b go *Egdes exist if tb dbits differ by 1 bit. *Q3 > vertices Pout :¢ Cy > Vertices = 4 . Edges: ed (i=2) , e2(2-3) 9 @3C 3-4) , e4(4- 15 a a_b d. 1) Minimum oo Fe AO DMP HM KP DO sO Stat} Q « o% © oD co oo 0 Poth: a | Q Yo B20 2. SO oO oie? A>Cad%e%g 2D QO “oa 306 Wee 2 s eaqasanieage Q Yo 30 6 Ic oe 22 © oo © b di O “a da 6¢ Te lid 0} 0 Ya 3a be Td Ild Ire £1 0 4a 3a 6c Wd Id Ie 18F 9] 0 4a 3a 6c Td Id Ie 16g v 0 Ya 30a 6c Td Id Qe 6g | Quecion ‘ be Port a: a b ra 2 Cieubod Grroph © a Port b: > Dame as Question 4, Port C: Vertices = 348 Edges = 597 Poxtc: > Question 1, Fort d: Question:6 j ry A a Prim’s Algorithm :- i 4 Edges | Cost “ Co,d)) = : (a.e)) 2 Got ag Gayl & 2 MSt— (a,b) Be Toto = © b. Kruskal's Algorithen = = Edge | ok \ | Cea 4 (o,e)) + (e,d)] 2 (a,e) y | Totol = 6 “Cone 4s > La Tricktker , Y = Wicker. =. X+V Yr = TVT = True - ~ Again Contradiction » Stokement InVabid- Hence, From Core D: : X he Soge and Y i a lrvickstey. Question .@ ats oes Todo isidouy = uF The weother is bod = W 1 will not teach ducrete = ~T Inverse: GE VW) W 2 P28 a) Converse: [> PJ T > (FAnwW) b) Contoypositive (~Q> ~P} ARVO ST > (“FN WD) cy Implicakions p(P>@ > ~CP) > ~Co] CFAwW) >T Question:4 P= A ina knight + P= A is a knove QeBpaknight » ~Q=B8 is a knove R=Cira knight , ~R=-C% a knowe "A Says rP VQ. + Boos QeP -C gays YR r Folse rlrue = Knight (K) » Mome (ND AM B@ICR) ~Pva QeP oR Ki ke T F 21 Kak | Ne ai 4; 31K N| Kk F % = “IK | N N ¥ F a s| Na ey Ay is F cl Ny we CE F 35 IN| NK] T a: ia BIN IN IN| T aE + > Row 9,6,7,8 bhoew A= knoue > Row 5.6/9.8 shew B . : ov Knowe ( fannie pee Mngt 
