東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Zonality in Graphs.

Bowling, Andrew.

FindBook

Google Book

Amazon

博客來

Zonality in Graphs.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Zonality in Graphs./
作者:	Bowling, Andrew.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2023,
面頁冊數:	87 p.
附註:	Source: Dissertations Abstracts International, Volume: 84-11, Section: B.
Contained By:	Dissertations Abstracts International84-11B.
標題:	Theoretical mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30313228
ISBN:	9798379546151

Zonality in Graphs.
Bowling, Andrew.

Zonality in Graphs. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 87 p.

Source: Dissertations Abstracts International, Volume: 84-11, Section: B.

Thesis (Ph.D.)--Western Michigan University, 2023.

This item must not be sold to any third party vendors.

Graph labeling and coloring are among the most popular areas of graph theory due to both the mathematical beauty of these subjects as well as their fascinating applications. While the topic of labeling vertices and edges of graphs has existed for over a century, it was not until 1966 when Alexander Rosa introduced a labeling, later called a graceful labeling, that brought the area of graph labeling to the forefront in graph theory. The subject of graph colorings, on the other hand, goes back to 1852 when the young British mathematician Francis Guthrie observed that the countries in a map of England could be colored with four colors so that every two adjacent countries are colored differently. This led to the Four Color Problem, which is the problem of determining whether the regions of every plane map can be colored with four or fewer colors in such a way that every two adjacent regions are colored differently. A computer aided solution for the Four Color Problem was announced in 1976 by Kenneth Appel and Wolfgang Haken, resulting in the famous Four Color Theorem. In 2014, the Australian physicist Cooroo Egan introduced a graph labeling referred to as a zonal labeling. A zonal labeling is a vertex labeling of a connected plane graph G with the two nonzero elements of the ring ℤ3 of integers modulo 3 such that the sum of the labels of the vertices on the boundary of every region of G is the zero element of ℤ3. A graph possessing a zonal labeling is a zonal graph. A related labeling, called an inner zonal labeling, is a labeling of the vertices of a plane graph G with the nonzero elements of ℤ3 such that the sum of the labels of the vertices on the boundary of every interior region of G is the zero element of ℤ3. A graph possessing an inner zonal labeling is an inner zonal graph. There is a close connection between the existence of zonal and inner zonal labelings of planar graphs and the Four Color Theorem. In this work, we study zonality and inner zonality for several well-known classes of graphs, determine which of these graphs are zonal or inner zonal, and present characterization results on the structures of zonal graphs. Furthermore, we investigate a relationship between zonal graphs and inner zonal graphs and establish a connection between inner zonal graphs and the Four Color Theorem.

ISBN: 9798379546151Subjects--Topical Terms:

3173530
Theoretical mathematics.
Subjects--Index Terms:

Cycle rank

Zonality in Graphs.
LDR:03490nmm a2200397 4500 001 2396543
005 20240611104326.5
006 m o d
007 cr#unu||||||||
008 251215s2023 ||||||||||||||||| ||eng d
020 $a 9798379546151
035 $a (MiAaPQ)AAI30313228
035 $a AAI30313228
040 $a MiAaPQ $c MiAaPQ
100 1 $a Bowling, Andrew. $3 3766235
245 1 0 $a Zonality in Graphs.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2023
300 $a 87 p.
500 $a Source: Dissertations Abstracts International, Volume: 84-11, Section: B.
500 $a Advisor: Zhang, Ping.
502 $a Thesis (Ph.D.)--Western Michigan University, 2023.
506 $a This item must not be sold to any third party vendors.
520 $a Graph labeling and coloring are among the most popular areas of graph theory due to both the mathematical beauty of these subjects as well as their fascinating applications. While the topic of labeling vertices and edges of graphs has existed for over a century, it was not until 1966 when Alexander Rosa introduced a labeling, later called a graceful labeling, that brought the area of graph labeling to the forefront in graph theory. The subject of graph colorings, on the other hand, goes back to 1852 when the young British mathematician Francis Guthrie observed that the countries in a map of England could be colored with four colors so that every two adjacent countries are colored differently. This led to the Four Color Problem, which is the problem of determining whether the regions of every plane map can be colored with four or fewer colors in such a way that every two adjacent regions are colored differently. A computer aided solution for the Four Color Problem was announced in 1976 by Kenneth Appel and Wolfgang Haken, resulting in the famous Four Color Theorem. In 2014, the Australian physicist Cooroo Egan introduced a graph labeling referred to as a zonal labeling. A zonal labeling is a vertex labeling of a connected plane graph G with the two nonzero elements of the ring ℤ3 of integers modulo 3 such that the sum of the labels of the vertices on the boundary of every region of G is the zero element of ℤ3. A graph possessing a zonal labeling is a zonal graph. A related labeling, called an inner zonal labeling, is a labeling of the vertices of a plane graph G with the nonzero elements of ℤ3 such that the sum of the labels of the vertices on the boundary of every interior region of G is the zero element of ℤ3. A graph possessing an inner zonal labeling is an inner zonal graph. There is a close connection between the existence of zonal and inner zonal labelings of planar graphs and the Four Color Theorem. In this work, we study zonality and inner zonality for several well-known classes of graphs, determine which of these graphs are zonal or inner zonal, and present characterization results on the structures of zonal graphs. Furthermore, we investigate a relationship between zonal graphs and inner zonal graphs and establish a connection between inner zonal graphs and the Four Color Theorem.
590 $a School code: 0257.
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Mathematics. $3 515831
653 $a Cycle rank
653 $a Dutch windmill
653 $a Four color theorem
653 $a Graph theory
653 $a Labelings
653 $a Zonality
690 $a 0642
690 $a 0405
710 2 $a Western Michigan University. $b Mathematics. $3 3766236
773 0 $t Dissertations Abstracts International $g 84-11B.
790 $a 0257
791 $a Ph.D.
792 $a 2023
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30313228