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(k,l)-遞歸極大平面圖的結(jié)構(gòu)

陳祥恩,  李婷

陳祥恩, 李婷. (k,l)-遞歸極大平面圖的結(jié)構(gòu)[J]. 電子與信息學(xué)報, 2018, 40(9): 2281-2286. doi: 10.11999/JEIT171021
引用本文: 陳祥恩, 李婷. (k,l)-遞歸極大平面圖的結(jié)構(gòu)[J]. 電子與信息學(xué)報, 2018, 40(9): 2281-2286. doi: 10.11999/JEIT171021
Xiang’en CHEN, Ting LI. The Structure of (k,l)-recursive Maximal Planar Graph[J]. Journal of Electronics & Information Technology, 2018, 40(9): 2281-2286. doi: 10.11999/JEIT171021
Citation: Xiang’en CHEN, Ting LI. The Structure of (k,l)-recursive Maximal Planar Graph[J]. Journal of Electronics & Information Technology, 2018, 40(9): 2281-2286. doi: 10.11999/JEIT171021

(k,l)-遞歸極大平面圖的結(jié)構(gòu)

doi: 10.11999/JEIT171021

  • 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)
詳細(xì)信息
    作者簡介:

    陳祥恩：男，1965年生，教授，主要研究方向?yàn)閳D論及其應(yīng)用

    李婷：女，1993年生，碩士生，研究方向?yàn)閳D論及其應(yīng)用

    通訊作者:

    陳祥恩　 chenxe@nwnu.edu.cn

  • 中圖分類號: O157.5

The Structure of (k,l)-recursive Maximal Planar Graph

  • College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Funds: The National Natural Science Foundation of China (11761064, 61163037, 61163054)
  • 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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  • 圖  1  階分別為4,7,10的遞歸極大平面圖

    圖  2  命題3所述圖的結(jié)構(gòu)

    圖  3  命題3證明過程中出現(xiàn)的遞歸極大平面圖

    圖  4  定理4證明過程中出現(xiàn)的遞歸極大平面圖

    圖  5  A型的(2,3)-遞歸極大平面圖

    圖  6  6階的B型(2,3)-遞歸極大平面圖

    圖  7  定理7證明里(1)中的B型(2,3)-遞歸極大平面圖

    圖  8  定理7證明里(2)中出現(xiàn)的(2,3)-遞歸極大平面圖

    圖  9  定理7證明里(2)中出現(xiàn)的另一個(2,3)-遞歸極大平面圖

    圖  10  C型的(2,3)-遞歸極大平面圖

    圖  11  A型遞歸極大平面圖

    圖  12  B型的(3,2)-遞歸極大平面圖

    圖  13  C型的(3,2)-遞歸極大平面圖

    圖  14  D型的(3,2)-遞歸極大平面圖

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出版歷程
  • 收稿日期:  2017-11-01
  • 修回日期:  2018-06-04
  • 網(wǎng)絡(luò)出版日期:  2018-07-12
  • 刊出日期:  2018-09-01

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