Recently, m-polar fuzzy graph (mPF graph) becomes a growing research topic as the generalization of fuzzy graph. In this paper, at first mPF path, mPF cycle in an mPF graph are defined. The strength of connectedness of mPF path is introduced. Next, strongest and strong mPF path, mPF bridges, mPF cut nodes, mPF tree and mPF forests in an mPF graph are considered. Also, it is proved that an arc of mPF tree is strong mPF arc if and only if it is an mPF bridge. Finally, mPF end nodes in an mPF graph is defined and investigated some properties of it. An application of strongest path problem in 3-polar fuzzy graph is also given at the end.
mPF graphs Strongest and strong mPF path mPF bridges mPF cut nodes mPF trees mPF forests
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The authors are highly thankful to the honorable Editor in Chief, Associate Editor and the honorable reviewers for their valuable suggestions which significantly improved the quality and representation of the paper. Financial support of first author by University Grants Commission, New Delhi, India(Fl-17.112014-15/RGNF-2014-15-SC-WES-63919(SA-Ill/Website)) is thankfully acknowledged.
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