Abstract
Abstract This study focuses on finding super edge-magic total (SEMT) labeling and deficiency of imbalanced fork and disjoint union of imbalanced fork with star, bistar and path; in addition, the SEMT strength for Imbalanced Fork is investigated.
Highlights
If a graph G allows at least one super edge-magic total (SEMT) labeling, the smallest of the magic constants for all possible distinct SEMT labelings of G describes SEMT strength, sm(G), of G
For any graph G, the SEMT deficiency, signified as μs(G), is the least number n of isolated vertices that we have to take in union with G so that the resulting graph G ∪ nK1 is SEMT, and the case +∞ will arise if no isolated vertex fulfills this criterion
We formulated the results on SEMT labeling and deficiency of forests consisting of imbalanced fork and disjoint union of imbalanced fork with star, bistar and path, respectively
Summary
If a graph G allows at least one SEMT labeling, the smallest of the magic constants for all possible distinct SEMT labelings of G describes SEMT strength, sm(G), of G. We formulated the results on SEMT labeling and deficiency of forests consisting of imbalanced fork and disjoint union of imbalanced fork with star, bistar and path, respectively.
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