Graph theory, and graph labeling in particular, are fast-growing research areas in mathematics. New results are constantly being discovered and published at a rapidly increasing rate due to the enormous number of open problems and conjectures in the field. This book deals mainly with the super edge-antimagic branch of graph labeling. It is written for specialists, but could be read also by postgraduate or undergraduate students with high school knowledge of mathematics and a vibrant interest in problem-solving.

The International J. Mathematical Combinatorics is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly, which publishes original research papers and survey articles in all aspects of mathematical combinatorics, Smarandache multi-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.

Magic and antimagic labelings are among the oldest labeling schemes in graph theory. This book takes readers on a journey through these labelings, from early beginnings with magic squares up to the latest results and beyond. Starting from the very basics, the book offers a detailed account of all magic and antimagic type labelings of undirected graphs. Long-standing problems are surveyed and presented along with recent results in classical labelings. In addition, the book covers an assortment of variations on the labeling theme, all in one self-contained monograph. Assuming only basic familiarity with graphs, this book, complete with carefully written proofs of most results, is an ideal introduction to graph labeling for students learning the subject. More than 150 open problems and conjectures make it an invaluable guide for postgraduate and early career researchers, as well as an excellent reference for established graph theorists.

This volume constitutes the refereed post-conference proceedings of the International Conference on Theoretical Computer Science and Discrete Mathematics, held in Krishnankoil, India, in December 2016. The 57 revised full papers were carefully reviewed and selected from 210 submissions. The papers cover a broad range of topics such as line graphs and its generalizations, large graphs of given degree and diameter, graphoidal covers, adjacency spectrum, distance spectrum, b-coloring, separation dimension of graphs and hypergraphs, domination in graphs, graph labeling problems, subsequences of words and Parike matrices, lambda-design conjecture, graph algorithms and interference model for wireless sensor networks.

Papers on Smarandache Lattice and Pseudo Complement, Smarandache’s Conjecture on Consecutive Primes, Signed Domatic Number of Directed Circulant Graphs, Generalized Quasi-Kenmotsu Manifolds, Geometry on Non-Solvable Equations-A Review on Contradictory Systems, and other topics. Contributors: Octavian Cira, Linfan Mao, N. Kannappa, K. Suresh, F. Smarandache, M. Ali, A. Raheem, A. Q. Baig, M. Javaid, Barnali Laha, Arindam Bhattacharyya, and others.

In this issue, there are 17 papers published: Paper 1: Bertrand curves pair, Smarandache curves Paper 2: Dual Lorentzian space, dual curve, dual curves of constant breadth, Bishop frame. Paper 3: (r,m, k)-regular fuzzy graph. Paper 4: edge-antimagic labeling. Paper 5: Ruled surfaces, curve, geodesic. Paper 6: Quarter-symmetric metric connection. Paper 7: Smarandachely k-signed graph. Paper 8: Common fixed point, rational expression. Paper 9: Smarandachely binding number. Paper 10: Wiener index, quasi-total graph. Paper 11: Transformation graph. Paper 12: Probabilistic bounds on weak and strong total domination in graphs. Paper 13; Smarandachely quotient cordial labeling. Paper 14: Nonholonomic Frames for Finsler Space. Paper 15: b-chromatic number of graphs. Paper 16: Strong defining numbers in graph. Paper 17: A Report on the Promoter Dr. Linfan Mao of Mathematical Combinatorics by your name.

Papers by many authors on subdivision of stars, Line digraph, cut vertex, Smarandachely k-domination number, Smarandachely transformation graph, Smarandachely super (a, d)-edge-antimagic total labeling, super (a, d)-EAT labeling, complete bipartite subdigraph, line cut vertex digraph, Smarandachely line cut vertex digraph and so on.

The mathematical combinatorics is a subject that applying combinatorial notion to all mathematics and all sciences for understanding the reality of things in the universe. The International J. Mathematical Combinatorics is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly, which publishes original research papers and survey articles in all aspects of mathematical combinatorics, Smarandache multi-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.

Numerous well-presented and important papers from the conference are gathered in the proceedings for the purpose of pointing directions for useful future research in diverse areas of mathematics including algebraic geometry, analysis, commutative algebra, complex analysis, discrete mathematics, dynamical systems, number theory and topology. Several papers on computational and applied mathematics such as wavelet analysis, quantum mechanics, piecewise linear modeling, cosmological models of super symmetry, fluid dynamics, interpolation theory, optimization, ergodic theory and games theory are also presented.

Aimed toward upper undergraduate and graduate students in mathematics, this book examines the foremost forms of graph labelings including magic, harmonious, and graceful labelings. An overview of basic graph theory concepts and notation is provided along with the origins of graph labeling. Common methods and techniques are presented introducing readers to links between graph labels. A variety of useful techniques are presented to analyze and understand properties of graph labelings. The classical results integrated with new techniques, complete proofs, numerous exercises, and a variety of open problems, will provide readers with a solid understanding of graph labelings.