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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 장전수학회 Proceedings of the Jangjeon Mathematical Society Proceedings of the Jangjeon Mathematical Society Vol.20 No.4
- 발행연도
- 2017.1
- 수록면
- 613 - 622 (10page)
이용수
초록· 키워드
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A graphoidal cover of a graph G is a collection Ψ of non- trivial paths (not necessarily open) in G such that every vertex of G is an internal vertex of at most one path in Ψ and every edge of G is in exactly one path in Ψ. A graphoidal cover Ψ of G is a truly non- trivial graphoidal cover (TNT graphoidal cover) of G if every path in Ψ has length greater than 1. A graph G is a truly nontrivial graph (TNT graph) if it possesses a TNT graphoidal cover. In this paper we intend to answer the fundamental question "Does every graph possess a TNT graphoidal cover ?", raised by Fred Roberts in first author's thesis re- port. After exhibiting the fact that not every graph possesses a TNT graphoidal cover, we could obtain some forbidden structures for a graph to be a TNT graph. And in the quest to find graphs having a TNT graphoidal cover, we could identify certain classes of trees and unicyclic graphs which are TNT graphs.
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참고문헌 (19)
참고문헌 신청
B. D. Acharya / 2007 / Further results on domination in graphoidally covered graphs / AKCE Int. J. Graphs Comb 4(2):127~138
B. D. Acharya / 2015 / On graphs whose graphoidal dom-ination number is one / AKCE Int. J. Graphs Comb. 12(2-3):133~140
B. Devadas Acharya / 1999 / Domination in graphoidal covers of a graph / Discrete Math. 206(1-3):3~33
B. Devadas Acharya / 1987 / Graphoidal covers and graphoidal cov-ering number of a graph / Indian J. Pure Appl. Math. 18(10):882~890
S. Arumugam / 1997 / Graph theory and its applications / Tata McGraw-Hill :1~28
B. D. Acharya / 2015 / On graphs whose graphoidal dom-ination number is one / AKCE Int. J. Graphs Comb. 12(2-3):133~140
B. Devadas Acharya / 1999 / Domination in graphoidal covers of a graph / Discrete Math. 206(1-3):3~33
B. Devadas Acharya / 1987 / Graphoidal covers and graphoidal cov-ering number of a graph / Indian J. Pure Appl. Math. 18(10):882~890
S. Arumugam / 1997 / Graph theory and its applications / Tata McGraw-Hill :1~28
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