An Introduction to Sumset Valued Graphs

In graph theory, graph labeling is an assignment of labels to the elements of a graph with respect to certain restrictions and in accordance with pre-specific rules. Graph labeling has become a fertile research area in graph theory for some decades. Different graph labelings are the result of different practical considerations. They are not only of theoretical interests but have many practical implications also. For many applications, the edges or vertices of a given graph are given labels that are meaningful in the context. This book discusses a particular type of set-labeling, called sumset labeling of graphs. As sumsets can be defined only for number sets, the study on sumset theory and hence the sumset labeling acquires their own beauty and restrictions. In the theory of sumset labeling, different set-labeled graphs are characterised in terms of the elements (numbers) contained in the set-labels, cardinalities of the set-labels and the structural properties of graphs in accordance with the sumset theory. We strongly believe that the study has immense potential and applicability in many practical or real-life situations.