Let [n]∗ denote the set of integers {−n−1 2 , . . . , n−1 2 } if n is odd, and {−n 2 , . . . , n 2 } \ {0} if n is even. A super edge-graceful labeling f of a graph G of order p and size q is a bijection f : E(G) → [q]∗, such that the induced vertex labeling f ∗ given by f ∗(u) = ∑ uv E(G) f(uv) is a bijection f ∗ : V (G) → [p]∗. A graph is super edge-graceful if it has a super edge-graceful la...

The traditional map labeling problems are mostly NP-hard. Hence, effective heuristics and approximations have been developed in the past. Recently, efficient algorithms for the so-called boundary labeling model have been introduced which assumes that the labels are placed on the boundary of the map and connected by polygonal leaders to their corresponding sites. Internal labels have been forbid...

Objectives: To identify a new family of Arithmetic sequential graceful graphs. Methods: The methodology involves mathematical formulation for labeling the vertices given graph and subsequently establishing that these formulations give rise to arithmetic labeling. Findings: In this study, we analyzed some star related graphs namely Star graph, Ustar, t-star, double proved possess Novelty: Here, ...

Labeling of genetically modified (GM) foods has increasingly become a topic at the consumer and policymaker level. Using an online survey that included conjoint analysis experiment, preference for GM labeling on both fresh tomatoes tomato plants was evaluated. Retailer (farmers market, grocery stores, mass merchandisers) sales quantity sold were simulated to examine impact introducing as well c...

This report describes the detailed procedures for Western blot analysis using fluorescent antibodies. After electrophoresis and subsequent electroblotting, the fluorescent-labeled antibodies were visible upon ultraviolet illumination of the polyvinylidene fluoride (PVDF) membranes and could then be photographed to give an accurate record of the blots. Fluorescent labeling allows for photographi...

We consider biobjective shortest path problems in networks with fuzzy arc lengths. Considering the available studies for single objective shortest path problems in fuzzy networks, using a distance function for comparison of fuzzy numbers, we propose three approaches for solving the biobjective prob- lems. The rst and second approaches are extensions of the labeling method to solve the sing...

In this paper, we focus on one type of labeling is called range labeling, have introduced for certain graphs as Pz, Cz, Sy,z(Double star), sun graph and some trees.