(k,l)-遞歸極大平面圖的結(jié)構(gòu)
doi: 10.11999/JEIT171021
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西北師范大學(xué)數(shù)學(xué)與統(tǒng)計學(xué)院 ??蘭州 ??730070
基金項(xiàng)目: 國家自然科學(xué)基金(11761064, 61163037, 61163054)
The Structure of (k,l)-recursive Maximal Planar Graph
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College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
Funds: The National Natural Science Foundation of China (11761064, 61163037, 61163054)
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摘要: 對于一個平面圖G實(shí)施擴(kuò)3-輪運(yùn)算是指在G的某個三角形面xyz內(nèi)添加一個新頂點(diǎn)v,使v與x, y, z均相鄰,最后得到一個階為|V(G)|+1的平面圖的過程。一個遞歸極大平面圖是指從平面圖K4出發(fā),逐次實(shí)施擴(kuò)3-輪運(yùn)算而得到的極大平面圖。 所謂一個(k,l)-遞歸極大平面圖是指一個遞歸極大平面圖,它恰好有k個度為3的頂點(diǎn),并且任意兩個3度頂點(diǎn)之間的距離均為l。該文對(k,l)-遞歸極大平面圖的存在性問題做了探討,刻畫了(3,2)-及(2,3)-遞歸極大平面圖的結(jié)構(gòu)。Abstract: For a maximal planar graph G, the operation of extending 3-wheel is a process from G to G∨v, where v is a new vertex embedded in some triangular face xyz of G and G∨v is a graph of order |V(G)|+1 obtained from G by connecting v to each one of x, y, z with one edge. A recursive maximal planar graph is a maximal planar graph obtained from K4 by extending 3-wheel continuously. A (k,l)-recursive maximal planar graph is a recursive maximal planar graph with exactly k vertices of degree 3 so that the distance between arbitrary two vertices of degree k is l. The existence of (k,l)-recursive maximal planar graph is discussed and the structures of (3,2)-as well as (2,3)-recursive maximal planar graphs are described.
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Key words:
- Planar graph /
- Maximal planar graph /
- Extending 3-wheel /
- Recursive maximal planar graph
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