Total Efficient Domination in Fuzzy Graphs

Xue-Gang Chen; Moo Young Sohn; De-Xiang Ma

doi:10.1109/ACCESS.2019.2948849

IEEE Access (Jan 2019)

Total Efficient Domination in Fuzzy Graphs

Xue-Gang Chen,
Moo Young Sohn,
De-Xiang Ma

Affiliations

Xue-Gang Chen: Department of Mathematics, North China Electric Power University, Beijing, China
Moo Young Sohn: ORCiD; Department of Mathematics, Changwon National University, Changwon, South Korea
De-Xiang Ma: Department of Mathematics, North China Electric Power University, Beijing, China

DOI: https://doi.org/10.1109/ACCESS.2019.2948849
Journal volume & issue: Vol. 7
pp. 155405 – 155411

Abstract

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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 $T$ or decide that $T$ has no total efficient dominating set.

Published in IEEE Access

ISSN: 2169-3536 (Online)
Publisher: IEEE
Country of publisher: United States
LCC subjects: Technology: Electrical engineering. Electronics. Nuclear engineering
Website: https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639

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