電大離散數(shù)學(xué)作業(yè)5答案(圖論部分)

1、 形成性考核作業(yè) 專(zhuān)業(yè)好文檔姓 名： 學(xué) 號(hào)： 得 分： 教師簽名： 離散數(shù)學(xué)作業(yè)5離散數(shù)學(xué)圖論部分形成性考核書(shū)面作業(yè)本課程形成性考核書(shū)面作業(yè)共3次，內(nèi)容主要分別是集合論部分、圖論部分、數(shù)理邏輯部分的綜合練習(xí)，基本上是按照考試的題型（除單項(xiàng)選擇題外）安排練習(xí)題目，目的是通過(guò)綜合性書(shū)面作業(yè)，使同學(xué)自己檢驗(yàn)學(xué)習(xí)成果，找出掌握的薄弱知識(shí)點(diǎn)，重點(diǎn)復(fù)習(xí)，爭(zhēng)取盡快掌握。本次形考書(shū)面作業(yè)是第二次作業(yè)，大家要認(rèn)真及時(shí)地完成圖論部分的綜合練習(xí)作業(yè)。要求：將此作業(yè)用a4紙打印出來(lái)，手工書(shū)寫(xiě)答題，字跡工整，解答題要有解答過(guò)程，要求2010年12月5日前完成并上交任課教師（不收電子稿）。并在05任務(wù)界面下方點(diǎn)擊“保存

2、”和“交卷”按鈕，以便教師評(píng)分。一、填空題1已知圖g中有1個(gè)1度結(jié)點(diǎn)，2個(gè)2度結(jié)點(diǎn)，3個(gè)3度結(jié)點(diǎn)，4個(gè)4度結(jié)點(diǎn)，則g的邊數(shù)是 15 2設(shè)給定圖g(如右由圖所示)，則圖g的點(diǎn)割集是 f 3設(shè)g是一個(gè)圖，結(jié)點(diǎn)集合為v，邊集合為e，則g的結(jié)點(diǎn) 度數(shù)之和 等于邊數(shù)的兩倍4無(wú)向圖g存在歐拉回路，當(dāng)且僅當(dāng)g連通且 等于出度 5設(shè)g=是具有n個(gè)結(jié)點(diǎn)的簡(jiǎn)單圖，若在g中每一對(duì)結(jié)點(diǎn)度數(shù)之和大于等于 n-1 ，則在g中存在一條漢密爾頓路 6若圖g=中具有一條漢密爾頓回路，則對(duì)于結(jié)點(diǎn)集v的每個(gè)非空子集s，在g中刪除s中的所有結(jié)點(diǎn)得到的連通分支數(shù)為w，則s中結(jié)點(diǎn)數(shù)|s|與w滿(mǎn)足的關(guān)系式為 w(g-v1) v1 7設(shè)完全

3、圖k有n個(gè)結(jié)點(diǎn)(n2)，m條邊，當(dāng) n為奇數(shù) 時(shí)，k中存在歐拉回路8結(jié)點(diǎn)數(shù)v與邊數(shù)e滿(mǎn)足 e=v-1 關(guān)系的無(wú)向連通圖就是樹(shù)9設(shè)圖g是有6個(gè)結(jié)點(diǎn)的連通圖，結(jié)點(diǎn)的總度數(shù)為18，則可從g中刪去 4 條邊后使之變成樹(shù)10設(shè)正則5叉樹(shù)的樹(shù)葉數(shù)為17，則分支數(shù)為i = 5 二、判斷說(shuō)明題（判斷下列各題，并說(shuō)明理由）1如果圖g是無(wú)向圖，且其結(jié)點(diǎn)度數(shù)均為偶數(shù)，則圖g存在一條歐拉回路(1) 不正確，缺了一個(gè)條件，圖g應(yīng)該是連通圖，可以找出一個(gè)反例，比如圖g是一個(gè)有孤立結(jié)點(diǎn)的圖。2如下圖所示的圖g存在一條歐拉回路(2) 不正確，圖中有奇數(shù)度結(jié)點(diǎn)，所以不存在是歐拉回路。3如下圖所示的圖g不是歐拉圖而是漢密爾頓圖

4、g 解：正確因?yàn)閳D中結(jié)點(diǎn)a，b，d，f的度數(shù)都為奇數(shù)，所以不是歐拉圖。如果我們沿著(a,d,g,f,e,b,c,a)，這樣除起點(diǎn)和終點(diǎn)是a外，我們經(jīng)過(guò)每個(gè)點(diǎn)一次僅一次，所以存在一條漢密爾頓回路，是漢密爾頓圖4設(shè)g是一個(gè)有7個(gè)結(jié)點(diǎn)16條邊的連通圖，則g為平面圖解：(1) 錯(cuò)誤假設(shè)圖g是連通的平面圖，根據(jù)定理，結(jié)點(diǎn)數(shù)v，邊數(shù)為e，應(yīng)滿(mǎn)足e小于等于3v-6，但現(xiàn)在16小于等于3*7-6，顯示不成立。所以假設(shè)錯(cuò)誤。 5設(shè)g是一個(gè)連通平面圖，且有6個(gè)結(jié)點(diǎn)11條邊，則g有7個(gè)面(2) 正確根據(jù)歐拉定理，有v-e+r=2，邊數(shù)v=11，結(jié)點(diǎn)數(shù)e=6，代入公式求出面數(shù)r=7三、計(jì)算題1設(shè)g=，v= v1，v2

5、，v3，v4，v5，e= (v1,v3)，(v2,v3)，(v2,v4)，(v3,v4)，(v3,v5)，(v4,v5) ，試(1) 給出g的圖形表示； (2) 寫(xiě)出其鄰接矩陣；(3) 求出每個(gè)結(jié)點(diǎn)的度數(shù)； (4) 畫(huà)出其補(bǔ)圖的圖形解：(1)oooov1ov5v2v3v4(2) 鄰接矩陣為(3) v1結(jié)點(diǎn)度數(shù)為1，v2結(jié)點(diǎn)度數(shù)為2，v3結(jié)點(diǎn)度數(shù)為3，v4結(jié)點(diǎn)度數(shù)為2，v5結(jié)點(diǎn)度數(shù)為2(4) 補(bǔ)圖圖形為oooov1ov5v2v3v42圖g=，其中v= a, b, c, d, e，e= (a, b), (a, c), (a, e), (b, d), (b, e), (c, e), (c, d),

6、(d, e) ，對(duì)應(yīng)邊的權(quán)值依次為2、1、2、3、6、1、4及5，試（1）畫(huà)出g的圖形； （2）寫(xiě)出g的鄰接矩陣；（3）求出g權(quán)最小的生成樹(shù)及其權(quán)值（1）g的圖形如下：（2）寫(xiě)出g的鄰接矩陣（3）g權(quán)最小的生成樹(shù)及其權(quán)值3已知帶權(quán)圖g如右圖所示 (1) 求圖g的最小生成樹(shù)； (2)計(jì)算該生成樹(shù)的權(quán)值解：(1) 最小生成樹(shù)為12357(2) 該生成樹(shù)的權(quán)值為(1+2+3+5+7)=184設(shè)有一組權(quán)為2, 3, 5, 7, 17, 31，試畫(huà)出相應(yīng)的最優(yōu)二叉樹(shù)，計(jì)算該最優(yōu)二叉樹(shù)的權(quán)35251071731173465權(quán)為 2*5+3*5+5*4+7*3+17*2+31=131四、證明題1設(shè)g是一個(gè)n

7、階無(wú)向簡(jiǎn)單圖，n是大于等于3的奇數(shù)證明圖g與它的補(bǔ)圖中的奇數(shù)度頂點(diǎn)個(gè)數(shù)相等證明：設(shè)，則是由n階無(wú)向完全圖的邊刪去e所得到的所以對(duì)于任意結(jié)點(diǎn)，u在g和中的度數(shù)之和等于u在中的度數(shù)由于n是大于等于3的奇數(shù)，從而的每個(gè)結(jié)點(diǎn)都是偶數(shù)度的（度），于是若在g中是奇數(shù)度結(jié)點(diǎn)，則它在中也是奇數(shù)度結(jié)點(diǎn)故圖g與它的補(bǔ)圖中的奇數(shù)度結(jié)點(diǎn)個(gè)數(shù)相等2設(shè)連通圖g有k個(gè)奇數(shù)度的結(jié)點(diǎn)，證明在圖g中至少要添加條邊才能使其成為歐拉圖證明：由定理3.1.2，任何圖中度數(shù)為奇數(shù)的結(jié)點(diǎn)必是偶數(shù)，可知k是偶數(shù)又根據(jù)定理4.1.1的推論，圖g是歐拉圖的充分必要條件是圖g不含奇數(shù)度結(jié)點(diǎn)因此只要在每對(duì)奇數(shù)度結(jié)點(diǎn)之間各加一條邊，使圖g的所有結(jié)點(diǎn)的

8、度數(shù)變?yōu)榕紨?shù)，成為歐拉圖故最少要加條邊到圖g才能使其成為歐拉圖if we dont do that it will go on and go on. we have to stop it; we need the courage to do it.his comments came hours after fifa vice-president jeffrey webb - also in london for the fas celebrations - said he wanted to meet ivory coast international toure to discuss his

9、 complaint.cska general director roman babaev says the matter has been exaggerated by the ivorian and the british media.blatter, 77, said: it has been decided by the fifa congress that it is a nonsense for racism to be dealt with with fines. you can always find money from somebody to pay them.it is

10、a nonsense to have matches played without spectators because it is against the spirit of football and against the visiting team. it is all nonsense.we can do something better to fight racism and discrimination.this is one of the villains we have today in our game. but it is only with harsh sanctions

11、 that racism and discrimination can be washed out of football.the (lack of) air up there watch mcayman islands-based webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will attend citys premier league match at chelsea on sunda

12、y.i am going to be at the match tomorrow and i have asked to meet yaya toure, he told bbc sport.for me its about how he felt and i would like to speak to him first to find out what his experience was.uefa hasopened disciplinary proceedings against cskafor the racist behaviour of their fans duringcit

13、ys 2-1 win.michel platini, president of european footballs governing body, has also ordered an immediate investigation into the referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian side added: we found no racist insults from fans of cska.bau

14、mgartner the disappointing news: mission aborted.the supersonic descent could happen as early as sunda.the weather plays an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. the

15、balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles

16、/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.the balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly step out onto something resembling an olympic diving platfo

17、rm.below, the earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. still, hell be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. it will be like he is diving into the shallow end.skydiver preps for the big

18、jumpwhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to earth. but this will not be enough to stop him completely.if he goes too fast or spins out of control, he has a stabilization parachute tha