Reverse super edge-magic strength of banana trees

A (p, q)–graph G is reverse super magic if there exists a bijection f : V ∪ E → {1, 2, …, p + q} such that is a constant for any edge uv ∈ E and f(E) = {l, 2, …, q}. Then f is a reverse super magic labeling of G. The reverse super magic strength of a reverse super magic graph G is defined as rsms (G) = min { is a reverse super magic labeling of G}. In this paper, a characterization of a triangle free reverse super magic graph to attain the lower bound of the reverse super magic strength has been obtained. Moreover, the reverse super magic strength of some new classes of graphs such as and has been computed.

Given a graph G with n vertices and m edges and an abelian group A of order equal to max(n,m). By labeling of A∗-vertex magic labeling and A∗-edge magic labeling we mean a pair one-to-one maps, one from V(G) to A, and another one from E(G) to A, rather than the bijection maps considered in the literature from V(G)∪E(G) to A, and new results were obtained.

A reverse magic labelling of a graph G(V, E) is a bijection f: V ∪ E → {1, 2, 3, ......, v + ε} such that for all edges xy, f(xy) - {f(x) + f(y)} is a constant which is denoted by c(f). A reverse magic labelling of a graph G(V, E) is called reverse super edge-magic labelling of G if f(V) = {1, 2, ...... v} and f(E) = {v + 1, v + 2, ......, v + ε}. The reverse super edge-magic strength of a graph G,rsm(G), is defined as the minimum of all c(f) where the minimum is taken over all reverse edge-magic labelling f of G. In this paper we invented the reverse super edge-magic strength of banana trees.

The application of Intuitionistic fuzzy total edge magic labelling to a graphical image at the 20th week of gestation provides insights into facilitates gender prediction as well as assessment of fetal blood flow on a second-trimester Doppler ultrasound screen. Ultrasounds screen the fetal heart rate during the 20th week of gestation using Doppler ultrasound for blood flow. A fetal heart rate above 2.5 beats per second suggests a female baby, while a rate less than 2.5 beats per second indicates a male baby. We convert the fetal heart blood flow into a graphical image and label it using intuitionistic fuzzy total edge magic labelling.