Bounds of Strong EMT Strength for certain Subdivision of Star and Bistar

• Main Authors: Kanwal Salma, Riasat Ayesha, Imtiaz Mariam, Iftikhar Zurdat, Javed Sana, Ashraf Rehana
• Format: Article
• Language: English
• Published: De Gruyter 2018-11-01
• Series: Open Mathematics
• Subjects: semt labeling; semt deficiency; semt strength; fork; h-tree; 05c78
• Online Access: https://doi.org/10.1515/math-2018-0111

A super edge-magic total (SEMT) labeling of a graph ℘(V, E) is a one-one map ϒ from V(℘)∪E(℘) onto {1, 2,…,|V (℘)∪E(℘) |} such that ∃ a constant “a” satisfying ϒ(υ) + ϒ(υν) + ϒ(ν) = a, for each edge υν ∈E(℘), moreover all vertices must receive the smallest labels. The super edge-magic total (SEMT) strength, sm(℘), of a graph ℘ is the minimum of all magic constants a(ϒ), where the minimum runs over all the SEMT labelings of ℘. This minimum is defined only if the graph has at least one such SEMT labeling. Furthermore, the super edge-magic total (SEMT) deficiency for a graph ℘, signified as μs(℘)$\mu_{s}(\wp)$ is the least non-negative integer n so that ℘∪nK1 has a SEMT labeling or +∞ if such n does not exist. In this paper, we will formulate the results on SEMT labeling and deficiency of fork, H -tree and disjoint union of fork with star, bistar and path. Moreover, we will evaluate the SEMT strength for trees.