Preface
Bull. Malays. Math. Sci. Soc.
Sandi Klavžar 0 1 2 3
Xueliang Li 0 1 2 3
Sanming Zhou 0 1 2 3
0 Center for Combinatorics and LPMC, Nankai University , Tianjin 300071 , People's Republic of China
1 Faculty of Natural Sciences and Mathematics, University of Maribor , Maribor , Slovenia
2 Faculty of Mathematics and Physics, University of Ljubljana , Ljubljana , Slovenia
3 School of Mathematics and Statistics, The University of Melbourne , Parkville, VIC 3010 , Australia

Published online: 26 January 2016
© Malaysian Mathematical Sciences Society and Universiti Sains Malaysia 2016
Graph theory is a young but rapidly maturing subject. It is an important branch of
modern mathematics in the information age with applications in a range of
disciplines such as computer science, communication, complex systems, combinatorial
optimization, chemistry, biology, to name only a few. Over the years the Bulletin of
the Malaysian Mathematical Sciences Society has published a number of papers in
graph theory, making it a noteworthy forum for researchers in the area. The Bulletin
constantly receives highquality submissions in graph theory as well as other
mathematical areas. To reflect recent developments in graph theory in a timely manner and
also to reduce the backlog of the Bulletin, we decided to edit this special issue on
graph theory.
This collection provides the graph theory community with twentysix papers
on a diversity of hot topics of current research interests. According to the topics
covered, we have grouped the papers into five parts. The first contains papers of
algebraic flavor, starting with a paper addressing graphs of ideals of a
commutative ring. The next contribution in this part discusses the cyclic edgeconnectivity of
vertextransitive graphs, doubleorbit graphs, and regular doubleorbit graphs. This is
followed by two papers on Cayley graphs and two more papers on Laplacian spectra of
graphs.
The second part of the present collection is filled with papers from metric graph
theory. One of the deepest topics studied in this area is the Gromov hyperbolicity,
and the first paper in this part gives a characterization of the hyperbolicity of periodic
graphs. In the subsequent paper the diameter of the neighborhood graph is studied
in terms of the diameter of the original graph. Then an axiomatic approach to metric
properties is taken by characterizing all graphs for which the induced path transit
function satisfies the socalled Pasch axiom. The last three papers on metric graph
theory are from one of the most active related areas, namely the theory of the metric
dimension. In these papers three variants of the metric dimension are studied: the
kmetric dimension, the local metric dimension, and the simultaneous strong metric
dimension, respectively.
The third part of this collection consists of four papers on graph domination. The
first studies total domination vertex critical graphs, while the second is concerned with
2rainbow domination and independent 2rainbow domination. The last two papers
on graph domination investigate the nonisolating bondage in graphs and the bondage
number of Mycielski graphs, respectively.
The fourth part is devoted to graph coloring and independence. This part also
contains four papers, of which the first two investigate neighbor sum distinguishing
edge colorings and equitable colorings, respectively. The last two papers are concerned
with the third largest number of maximal independent sets in graphs and maximum
induced matchings in hexagonal graphs, respectively.
The special issue is concluded with six papers that cover additional themes of
graph theory. The first two of them investigate signed graphs with a focus on signed
line graphs. In the subsequent paper fractional critical deleted graphs are studied. This
is followed by a paper on the harmonic index, which is a degreebased graph invariant.
The fifth paper in the last part investigates embeddings of arbitrary trees into graceful
trees, while the last paper is concerned with the intrinsic structure of iterated line
graphs.
We hope that this collection will attract a wide audience of researchers in graph
theory and related disciplines. Enjoy reading!