Total Efficient Domination in Fuzzy Graphs
This study proposed total efficient domination in fuzzy graphs. The exact values on the total efficient domination number for several classes of fuzzy graphs are determined. A lower bound and an upper bound for the total efficient domination number in terms of maximum strong arc neighborhood degree...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IEEE
2019-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/8879555/ |
| _version_ | 1811274120471511040 |
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| author | Xue-Gang Chen Moo Young Sohn De-Xiang Ma |
| author_facet | Xue-Gang Chen Moo Young Sohn De-Xiang Ma |
| author_sort | Xue-Gang Chen |
| collection | DOAJ |
| description | This study proposed total efficient domination in fuzzy graphs. The exact values on the total efficient domination number for several classes of fuzzy graphs are determined. A lower bound and an upper bound for the total efficient domination number in terms of maximum strong arc neighborhood degree and the order are obtained. In addition, a new relationship between total efficient domination number and total efficient domatic number is established. Finally, we design an algorithm to determine the minimum fuzzy cardinality of the total efficient dominating set of a fuzzy tree <inline-formula> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula> or decide that <inline-formula> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula> has no total efficient dominating set. |
| first_indexed | 2024-04-12T23:12:06Z |
| format | Article |
| id | doaj.art-d674f233f7b0489dba35fc982a4aeca6 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-12T23:12:06Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-d674f233f7b0489dba35fc982a4aeca62022-12-22T03:12:46ZengIEEEIEEE Access2169-35362019-01-01715540515541110.1109/ACCESS.2019.29488498879555Total Efficient Domination in Fuzzy GraphsXue-Gang Chen0Moo Young Sohn1https://orcid.org/0000-0002-8761-9601De-Xiang Ma2Department of Mathematics, North China Electric Power University, Beijing, ChinaDepartment of Mathematics, Changwon National University, Changwon, South KoreaDepartment of Mathematics, North China Electric Power University, Beijing, ChinaThis study proposed total efficient domination in fuzzy graphs. The exact values on the total efficient domination number for several classes of fuzzy graphs are determined. A lower bound and an upper bound for the total efficient domination number in terms of maximum strong arc neighborhood degree and the order are obtained. In addition, a new relationship between total efficient domination number and total efficient domatic number is established. Finally, we design an algorithm to determine the minimum fuzzy cardinality of the total efficient dominating set of a fuzzy tree <inline-formula> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula> or decide that <inline-formula> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula> has no total efficient dominating set.https://ieeexplore.ieee.org/document/8879555/Fuzzy graphfuzzy treetotal efficient dominating set |
| spellingShingle | Xue-Gang Chen Moo Young Sohn De-Xiang Ma Total Efficient Domination in Fuzzy Graphs IEEE Access Fuzzy graph fuzzy tree total efficient dominating set |
| title | Total Efficient Domination in Fuzzy Graphs |
| title_full | Total Efficient Domination in Fuzzy Graphs |
| title_fullStr | Total Efficient Domination in Fuzzy Graphs |
| title_full_unstemmed | Total Efficient Domination in Fuzzy Graphs |
| title_short | Total Efficient Domination in Fuzzy Graphs |
| title_sort | total efficient domination in fuzzy graphs |
| topic | Fuzzy graph fuzzy tree total efficient dominating set |
| url | https://ieeexplore.ieee.org/document/8879555/ |
| work_keys_str_mv | AT xuegangchen totalefficientdominationinfuzzygraphs AT mooyoungsohn totalefficientdominationinfuzzygraphs AT dexiangma totalefficientdominationinfuzzygraphs |