### Foreword to the Special Focus on Graph Theory and Applications

Bharati Rajan, Ibrahim Venkat, K. G. Subramanian
2016 Mathematics in Computer Science
Graph theory is a fascinating branch of mathematics which has been developed with contributions from Euler, Kirchoff, Cayley, Hamilton, and many others. It is the Swiss mathematician Euler who is credited for having introduced the concept of a graph in solving the famous bridge problem. Many efficient graph algorithms have been developed in the past decade, e.g., for the shortest path problem and the connector problem arising in road and rail networks, the optimal assignment problem in the
more » ... xt of job assigning, and other such problems of practical interest, though there are graph-related problems such as the well-known travelling salesman problem which are NP-complete. The present-day applications of graph concepts and algorithms are in abundance. With an objective to provide a forum for researchers working on problems admitting graph formulations, in well-trodden as well as newer areas, to share their research findings and to benefit from their interactions with experts in the field of graph theory, the School of Computer Science at Universiti Sains Malaysia, Penang organised an International Workshop on Graph Algorithms (IWGA) in May 2015. The special focus on Graph Theory and Applications in this issue of Mathematics in Computer Science (MCS) contains the revised and enhanced versions of six papers selected from those presented at IWGA 2015. These papers have undergone the usual review-revision process of MCS. The paper by Bera and Mahalingam explores structural properties of words with a novel approach of relating two apparently different notions: graph and Parikh matrix of a word, a concept that has been introduced recently in the study of numerical properties of words. The authors introduce a new class of graphs, called Parikh word representable graphs, based on the concept of Parikh matrix which provides counts of suitable subwords that are subsequences of a given word. A major result established by the authors is a characterization of these graphs when the words are over a binary alphabet. The authors point out that the problem of characterization is open when the size of the alphabet is greater than two.