Deficiency of forests

• DOI: 10.1515/math-2017-0122
• Publication Date: 2017-12-13T08:00:49Z
• Authors: Sana Javed; Mujtaba Hussain; Ayesha Riasat; Salma Kanwal; Mariam Imtiaz; M. O. Ahmad
• Keywords: Artificial intelligence; comb; 0102 computer and information sciences; Graph Labeling; 2-sided generalized comb; Quantum mechanics; 01 natural sciences; Graph; MAGIC (telescope); Optical Code Division Multiple Access; Antimagic Labeling; super edge magic total labeling; Engineering; Number theory; QA1-939; FOS: Electrical engineering, electronic engineering, information engineering; FOS: Mathematics; 05c78; Conjecture; Electrical and Electronic Engineering; Graph Labeling and Dimension Problems; forests; Physics; Edge Coloring; Total Edge Irregularity; Discrete mathematics; bistar; Computer science; Programming language; Enhanced Data Rates for GSM Evolution; Computational Theory and Mathematics; Combinatorics; deficiency of graph; Computer Science; Physical Sciences; Integer (computer science); Mathematics

Abstract An edge-magic total labeling of an (n,m)-graph G = (V,E) is a one to one map λ from V(G) ∪ E(G) onto the integers {1,2,…,n + m} with the property that there exists an integer constant c such that λ(x) + λ(y) + λ(xy) = c for any xy ∈ E(G). It is called super edge-magic total labeling if λ (V(G)) = {1,2,…,n}. Furthermore, if G has no super edge-magic total labeling, then the minimum number of vertices added to G to have a super edge-magic total labeling, called super edge-magic deficiency of a graph G, is denoted by μs(G) [4]. If such vertices do not exist, then deficiency of G will be + ∞. In this paper we study the super edge-magic total labeling and deficiency of forests comprising of combs, 2-sided generalized combs and bistar. The evidence provided by these facts supports the conjecture proposed by Figueroa-Centeno, Ichishima and Muntaner-Bartle [2].