Set sequential graphs
An assignment f of distinct nonempty subsets of a finite set X to the vertices of a given graph \(G=(V,E)\) so that the values \(f\dot +(e)\), \(e=uv\), obtained as the symmetric differences \(f(u)\dot +f(v)\) of the subsets f(u) and f(v) of X, also are all distinct is called a set indexer of G. A set indexer f of G is called a segregation of X on G if the sets \(\{\) f(u): \(u\in V(G)\}\) and \(\{f\dot +(e):\) \(e\in E(G)\}\) are disjoint, and if, in addition, their union is the set \(Y(X)=2^ X-\{\phi \}\) of all the nonempty subsets of X then f is called a set sequential labeling of G. A graph is then called set sequential if it admits a set sequential labeling with respect to some set X. Inspired by an extensive study of assignments of subsets of a set to the elements of a graph and their applications due to the first author, we report here first hand investigations on our yet new notions of set sequential labelings of a graph.
scientific article; zbMATH DE number 4070960