形成性考核 作業(yè) 1 電大 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”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)完全圖 Kn有 n 個(gè)結(jié)點(diǎn) (n2)， m 條 邊， 當(dāng) n 為奇數(shù) 時(shí)， Kn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 姓 名： 學(xué) 號(hào)： 得 分： 教師簽名： 形成性考核 作業(yè) 2 (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 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， 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) G v1 v5 v2 v3 v4 形成性考核 作業(yè) 3 (2) 鄰接矩陣為 0110010110110110110000100 (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 2 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), (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 v1 v5 v2 v3 v4 形成性考核 作業(yè) 4 （ 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 (2) 該生成樹(shù)的權(quán)值為 (1+2+3+5+7)=18 4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) 1 2 3 5 7 形成性考核 作業(yè) 5 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 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 G 中的奇數(shù)度頂點(diǎn)個(gè)數(shù)相等 證明： 設(shè) ,G V E ， ,G V E 則 E 是由 n 階無(wú)向完全圖nK的邊刪去 E 所得到的所以對(duì)于任意結(jié)點(diǎn) uV ， u 在 G 和 G 中的度數(shù)之和等于 u 在nK中的度數(shù)由于 n 是大于等于 3 的奇數(shù)，從而nK的每個(gè)結(jié)點(diǎn)都是偶數(shù)度的（ 1 ( 2)n 度），于是若 uV 在 G 中是奇數(shù)度結(jié)點(diǎn)，則它在 G 中也是奇數(shù)度結(jié)點(diǎn)故圖 G 與它的補(bǔ)圖 G 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2k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)的度數(shù)變?yōu)榕紨?shù)，成為歐拉圖 故最少要加2k條邊到圖 G 才能使其成為歐拉圖 3 5 2 5 10 7 17 31 17 34 65 形成性考核 作業(yè) 6 請(qǐng)您刪除一下內(nèi)容， O( _ )O 謝謝！ 2015 年中央電大期末復(fù)習(xí)考試小抄大全，電大期末考試必備小抄，電大考試必過(guò)小抄 After earning his spurs in the kitchens of The Westin, The Sheraton, Sens on the Bund, and a sprinkling of other top-notch venues, Simpson Lu fi nally got the chance to become his own boss in November 2010. Sort of. The Shanghai-born chef might not actually own California Pizza Kitchen (CPK) but he is in sole charge of both kitchen and frontof- house at this Sinan Mansionsstalwart. Its certainly a responsibility to be the head chef, and then to have to manage the rest of the restaurant as well, the 31-year-old tells Enjoy Shanghai. In hotels, for example, these jobs are strictly demarcated, so its a great opportunity to learn how a business operates across the board. It was a task that management back in sunny California evidently felt he was ready for, and a vote of confi dence from a company that, to date, has opened 250 outlets in 11 countries. And for added pressure, the Shanghai branch was also CPKs China debut. For sure it was a big step, and unlike all their other Asia operations that are franchises, they decided to manage it directly to begin with, says Simpson. Two years ago a private franchisee took over the lease, but the links to CPK headquarters are still strong, with a mainland-based brand ambassador on hand to ensure the business adheres to its ethos of creating innovative, hearth-baked pizzas, a slice of PR blurb that Simpson insists lives up to the hype. They are very innovative, he says. The problem with most fast food places is that they use the same sauce on every pizza and just change the toppings. Every one of our 16 pizza sauces is a unique recipe that has been formulated to complement the toppings perfectly. The largely local customer base evidently agrees and on Saturday and Sunday, at least, the place is teeming. The kids-eat-for-free policy at weekends is undoubtedly a big draw, as well as is the spacious second-fl oor layout overlooked by a canopy of green from Fuxing Park over the road. The company is also focusing on increasing brand recognition and in recent years has taken part in outside events such as the regular California Week. Still, the sta are honest enough to admit that business could be better； as good, in fact, as in CPKs second outlet in the popular Kerry Parkside shopping mall in Pudong. Sinan Mansions has really struggled to get the number of visitors that were envisaged when it first opened, and it hasnt been easy for any of the tenants here, adds Simpson. Were planning a third outlet in the city in 2015, and we will probably choose a shopping mall again because of the better foot traffic. The tearooms once frequented by Coco Chanel and Marcel Proust are upping sticks and coming to Shanghai, Xu Junqian visits the Parisian outpost with sweet treats. One thing the century-old Parisian tearoom Angelina has shown is that legendary fashion designer Coco Chanel not only had style and glamor but also boasted great taste in food, pastries in particular. One of the most popular tearooms in Paris, Angelina is famous for having once been frequented by celebrities such as Chanel and writer Marcel Proust. Now Angelina has packed up its French ambience, efficient service, and beautiful, comforting desserts and flown them to Shanghai. At the flagship dine-in and take-out space in Shanghai, everything mimics the original tearoom designed from the beginning of the 20th century, in Paris, the height of Belle Epoque. The paintings on the wall, for example, are exactly the same as the one that depicts the landscape of southern France, the hometown of the owner； and the small tables are intentional imitations of the ones that Coco Chanel once sat at every afternoon for hot chocolate. The famous hot chocolate, known as LAfricain, is a luxurious mixture of four types of cocoa beans imported from Africa, blended in Paris and then shipped to Shanghai. Its sinfully sweet, rich and thick as if putting a bar of melting chocolate directly on the tongue and the fresh whipped cream on the side makes a light, but equally gratifying contrast. It is also sold in glass bottles as takeaway. The signature Mont-Blanc chestnut cake consists of three parts: the pureed chestnut on top, the vanilla cream like stuffing, and the meringue as base. Get all three layers in one scoop, not only for the different textures but also various flavors of sweetness. The dessert has maintained its popularity for a century, even in a country like France, perhaps the worlds most competitive place for desserts. A much overlooked pairing, is the Paris-New York choux pastry and N226 chocolate flavored tea. The choux pastry is a mouthful of airy pecan-flavored whipped cream, while the tea, a blend of black teas from China and Ceylon, cocoa and rose petals, offers a more subtle fragrance of flowers and chocolate. Ordering these two items, featuring a muted sweetness, makes it easier for you to fit into your little black dress. Breakfast, brunch, lunch and light supper are also served at the tearoom, a hub of many cultures and takes in a mix of different styles of French cuisines, according to the management team. The semi-cooked foie gras terrine, is seductive and deceptive. Its generously served at the size and shape of a toast, while the actual brioche toast is baked into a curved slice dipped with fig chutney. The flavor, however, is honest: strong, smooth and sublime. And you dont actually need the toast for crunchiness. This is the season for high teas, with dainty cups of fine china and little pastries that appeal to both visual and physical appetites. But there is one high tea with a difference, and Pauline D. Loh finds out just exactly why it is special. Earl Grey tea and macarons are all very well for the crucial recuperative break in-between intensive bouts of holiday season shopping. And for those who prefer savory to sweet, there is still the selection of classic Chinese snacks called dim sum to satisfy and satiate. High tea is a meal to eat with eye and mouth, an in-between indulgence that should be light enough not to spoil dinner, but sufficiently robust to take the edge off the hunger that strikes hours after lunch. The afternoon tea special at Shang-Xi at the Four Seasons Hotel Pudong has just the right elements. It is a pampering meal, with touches of luxury that make the high tea session a treat in itself. Whole baby abalones are braised and then topped on a shortcrust pastry shell, a sort of Chinese version of the Western vol-au-vent, but classier. Even classier is the dim sum staple shrimp dumpling or hargow, upgraded with the addition of slivers of midnight dark truffles. This is a master touch, and chef Simon Choi, who presides unchallenged at Shang-Xi, has scored a winner again. Sweet prawns and aromatic truffles whats not to love? His masterful craftsmanship is exhibited in yet another pastry a sweet pastry that is shaped to look like a walnut, but which you can put straight into the mouth. It crumbles immediately, and the slightly sweet, nutty morsel is so easy to eat youll probably reach straight for another. My favorite is the dessert that goes by the name yangzhi ganlu, or ambrosia 形成性考核 作業(yè) 7 from the gods. The hotel calls it chilled mango cream with sago, pomelo and birds nest made with ingredients that resonate with every female soul. It does taste like ambrosia, with the sweet-sour fragrance of the mango forming the first layer of taste and sensation, and the pomelo sacs and sago pearls providing the tactile contrast. The birds