基本介紹
![出度](/img/7/19c/wZwpmLxQjNycDN4YTO2UzM1UTM1QDN5MjM5ADMwAjMwUzL2kzL1QzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![出度](/img/e/79f/wZwpmLwQDM1ETM5ATMzEzM1UTM1QDN5MjM5ADMwAjMwUzLwEzL1EzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![出度](/img/0/ffc/wZwpmL0ETO3ITO2QTMzEzM1UTM1QDN5MjM5ADMwAjMwUzL0EzL0gzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
在無向圖中,頂點所具有的邊的數目稱為頂點的 度。如圖1(a)中.無向圖的頂點的度為3,頂點的度為2。
![出度](/img/e/8b4/wZwpmLzIDN1cjM4gTN2UzM1UTM1QDN5MjM5ADMwAjMwUzL4UzLxgzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![出度](/img/0/ffc/wZwpmL0ETO3ITO2QTMzEzM1UTM1QDN5MjM5ADMwAjMwUzL0EzL0gzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![出度](/img/0/ffc/wZwpmL0ETO3ITO2QTMzEzM1UTM1QDN5MjM5ADMwAjMwUzL0EzL0gzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
在有向圖中,以頂點為頭的邊的數目稱為該頂點的 入度;以頂點為尾的邊的數目稱為該頂點的 出度;一個頂點的入度與出度之和稱為該頂點的 度。如圖1中,有向圖的頂點的入度為2,出度也是2,頂點的度則為4。
![圖1(a)G₁](/img/6/93c/wZwpmLycDM3gDO4gDO2UzM1UTM1QDN5MjM5ADMwAjMwUzL4gzLxAzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![圖1(b)G₂](/img/e/5b4/wZwpmLyEzM5ITM5EzN2UzM1UTM1QDN5MjM5ADMwAjMwUzLxczL2AzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![出度](/img/5/ea1/wZwpmLxAzN2MjM5cTO4kzM0UTMyITNykTO0EDMwAjMwUzL3kzL2AzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![出度](/img/a/e3f/wZwpmL1AzN1kDO3ATMwEDN0UTMyITNykTO0EDMwAjMwUzLwEzL4UzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![出度](/img/8/d3a/wZwpmLxIjM0ADOwQjN2UzM1UTM1QDN5MjM5ADMwAjMwUzL0YzL3AzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
設無向圖有個頂點,e條邊,每個頂點的度為,則有 :
![出度](/img/d/311/wZwpmLzADMzAjN4cDO2UzM1UTM1QDN5MjM5ADMwAjMwUzL3gzLxczLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
相關概念
圖的定義
![出度](/img/5/ea1/wZwpmLxAzN2MjM5cTO4kzM0UTMyITNykTO0EDMwAjMwUzL3kzL2AzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![出度](/img/1/2e5/wZwpmLyYDMzgzMwMzMzIDN0UTMyITNykTO0EDMwAjMwUzLzMzL1IzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![出度](/img/b/b17/wZwpmLyIDN2UTN1MzNwIDN0UTMyITNykTO0EDMwAjMwUzLzczL1MzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![出度](/img/b/ce7/wZwpmL3QjMwMzNzQTMxMzM1UTM1QDN5MjM5ADMwAjMwUzL0EzLxMzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
一個圖由一個非空有限頂點集和一個邊的有限集組成。圖的頂點集和邊集分別用和表示,則圖G可表示成。
![出度](/img/3/cf2/wZwpmL0MjN3gDN4cjN2UzM1UTM1QDN5MjM5ADMwAjMwUzL3YzLyQzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![出度](/img/d/e6c/wZwpmL3MzMyYjNzQDO2UzM1UTM1QDN5MjM5ADMwAjMwUzL0gzLzUzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![出度](/img/7/c9e/wZwpmL0cTM1YDM5UDO2UzM1UTM1QDN5MjM5ADMwAjMwUzL1gzL1IzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![出度](/img/4/bb0/wZwpmL4cjM1kDNzQzN2UzM1UTM1QDN5MjM5ADMwAjMwUzL0czL0YzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![出度](/img/7/c9e/wZwpmL0cTM1YDM5UDO2UzM1UTM1QDN5MjM5ADMwAjMwUzL1gzL1IzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![出度](/img/4/bb0/wZwpmL4cjM1kDNzQzN2UzM1UTM1QDN5MjM5ADMwAjMwUzL0czL0YzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![出度](/img/3/cf2/wZwpmL0MjN3gDN4cjN2UzM1UTM1QDN5MjM5ADMwAjMwUzL3YzLyQzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![出度](/img/d/e6c/wZwpmL3MzMyYjNzQDO2UzM1UTM1QDN5MjM5ADMwAjMwUzL0gzLzUzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![出度](/img/3/cf2/wZwpmL0MjN3gDN4cjN2UzM1UTM1QDN5MjM5ADMwAjMwUzL3YzLyQzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![出度](/img/3/cf2/wZwpmL0MjN3gDN4cjN2UzM1UTM1QDN5MjM5ADMwAjMwUzL3YzLyQzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![出度](/img/d/a08/wZwpmLzcDN0cDN4cjN2UzM1UTM1QDN5MjM5ADMwAjMwUzL3YzL3czLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
在圖中,若每條邊都用箭頭指明了方向,則稱此圖為 有向圖,否則為 無向圖。有向圖中的邊用表示,其中是有向圖的兩個頂點,稱為尾,稱為頭,在有向圖中用從到的箭頭表示,見圖2(a)。無向圖中的邊用表示,為無向圖的兩個頂點。圖2(b)是無向圖。無向圖的邊是無序的,也就是說與表示同一條邊。
![出度](/img/9/9f1/wZwpmLxgzNyUzNyMjM0EDN0UTMyITNykTO0EDMwAjMwUzLzIzLwgzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![出度](/img/9/9f1/wZwpmLxgzNyUzNyMjM0EDN0UTMyITNykTO0EDMwAjMwUzLzIzLwgzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![出度](/img/f/97c/wZwpmL4QzM5QzN0cDO2UzM1UTM1QDN5MjM5ADMwAjMwUzL3gzLzczLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
從圖2中可知,(b)是一棵樹,而(a)不是樹,所以說樹是圖的特例。具有n個頂點的無向圖,若有條邊,稱之為 完全圖。圖2中(c)便是一個完全圖。具有n個頂點的無向圖,至多有條邊;具有n個頂點的有向圖,則至多有條邊 。
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子圖
![出度](/img/7/19c/wZwpmLxQjNycDN4YTO2UzM1UTM1QDN5MjM5ADMwAjMwUzL2kzL1QzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![出度](/img/e/79f/wZwpmLwQDM1ETM5ATMzEzM1UTM1QDN5MjM5ADMwAjMwUzLwEzL1EzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![出度](/img/5/a10/wZwpmLyADN0kjM2MzNwIDN0UTMyITNykTO0EDMwAjMwUzLzczL0IzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![出度](/img/e/8b4/wZwpmLzIDN1cjM4gTN2UzM1UTM1QDN5MjM5ADMwAjMwUzL4UzLxgzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![出度](/img/0/ffc/wZwpmL0ETO3ITO2QTMzEzM1UTM1QDN5MjM5ADMwAjMwUzL0EzL0gzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![出度](/img/b/739/wZwpmLyczM5gzM2MzNwIDN0UTMyITNykTO0EDMwAjMwUzLzczL2czLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
設圖的頂點集和邊集為和,圖的頂點集和邊集為和,若:
![出度](/img/a/b9c/wZwpmL1ADO0cjN3QjN2UzM1UTM1QDN5MjM5ADMwAjMwUzL0YzL4YzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![出度](/img/e/8b4/wZwpmLzIDN1cjM4gTN2UzM1UTM1QDN5MjM5ADMwAjMwUzL4UzLxgzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![出度](/img/7/19c/wZwpmLxQjNycDN4YTO2UzM1UTM1QDN5MjM5ADMwAjMwUzL2kzL1QzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![出度](/img/b/bd8/wZwpmL4UTOxMDOyQjN2UzM1UTM1QDN5MjM5ADMwAjMwUzL0YzLzMzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![出度](/img/7/19c/wZwpmLxQjNycDN4YTO2UzM1UTM1QDN5MjM5ADMwAjMwUzL2kzL1QzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![出度](/img/1/03e/wZwpmL2gDN1kDO1kTN2UzM1UTM1QDN5MjM5ADMwAjMwUzL5UzL2QzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![出度](/img/d/5d6/wZwpmLyETNygTNwADN3UzM1UTM1QDN5MjM5ADMwAjMwUzLwQzLwYzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
則稱圖是圖的子圖。例如,圖2中圖是圖的子圖,圖是圖的子圖 。