| dc.description.abstract | A network topology (either communication network in
general or a network in a computer) can be modeled as a graph or a
directed graph (digraph, for short), where each processing element
is represented by a vertex and the connection between two processing
elements is represented by an edge (or, in the case of a digraph, by
a directed arc). The number of vertices is called the order of the
graph or digraph. The number of connections incident to a vertex is
called the degree of the vertex. If the connections are one way only
then we distinguish between in-coming and out-going connections and
we speak of the in-degree and the out-degree of a vertex. The
distance between two vertices is the length of the shortest path,
measured by the number of edges or arcs that need to be traversed in
order to reach one vertex from another vertex. In either case, the
largest distance between any two vertices, called the diameter of
the graph or digraph, represents the maximum data communication
delay in a communication network.
By this terminology, there are a wide range of study of graph theory
among mathematicians, even more when it is related to the recent
digital and internet technology. A dynamical communication, flexible
and massive (a huge number of elements which should be connected) is
the main requirement of this network technology development. The
complexity of the network will increase dramatically if the number
of elements (or computer) that are involved in the network
increases, especially if the number of connections that are
connected to a point is also getting larger, then the network with
efficient and high-speed, reliable, a good modularity, a good fault
tolerance and low vulnerability will always be a major concern in
designing the topology of network. One of the important efforts that
can be done is to do labeling of the network topology. In other word
we can do a graph labeling.
Furthermore, with an application of network technology in all
aspects of modern society, it leads to the disconnected topological
networks. However, obtaining a national or international publication
related to the labeling for disconnected graph is still relatively
few, see Gallian Dynamic Survey of Labeling. Practically it has been
begun since 2004. Therefore, in this book we will present a new
result for family of disconnected graph labeling such as Cycle,
Path, Caterpillar, Complete n-partite Graph, Star , Crown,
Triangular Lader, Generalized Petersen Graph, Banana Tree,
Firecracker, Graph Lobster, Generalized web, Graph E, Diamond
Ladder, Mountain Graph, Triangluar Book, Cycles non isomorphic with
a chord, and stair.
This book presents some collections of new effort of studying super
edge antimagic of disconnected graph in which it contains a new
results as well as an open problem that can be used as references to
other researchers in conducting research in labeling. This book was
inspired by a book written by Martin Baca and Mirka Miler with a
title of Super Edge Antimagic Labeling. They published that book in
America but it was not focused on studying a disconnected graph,
whereas in this book we only discus a disconnected graph.
The author is now carrying on going project concerning a labeling of
disconnected graph family so that in subsequent editions of this
book will present some more result of disconnected graph labeling
and continuously update it every year | en_US |
