2014/06/06 by N. K. Sudev, Sudev, N. K., K. A. Germina +1
Mathematics · #05C78 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C78
paper · pdf · doi:10.48550/arxiv.1407.5028
11 pages, 2 figures, submitted. arXiv admin note: substantial text overlap with arXiv:1403.3984, arXiv:1407.4533
arxiv created 2014/11/17 · arxiv updated 2014/11/18
A set-labeling of a graph G is an injective function f:V(G)→ P(X), where X is a finite set of non-negative integers and a set-indexer of G is a set-labeling such that the induced function f⊕:E(G)→ P(X)-\∅\ defined by f⊕(uv) = f(u)⊕f(v) for every uv∈ E(G) is also injective. A set-indexer f:V(G)→ P(X) is called a set-sequential labeling of G if f⊕(V(G)∪ E(G))=P(X)-\∅\. A graph G which admits a set-sequential labeling is called a set-sequential graph. An integer additive set-labeling is an injective function f:V(G)→ P(ℕ0), ℕ0 is the set of all non-negative integers and an integer additive set-indexer is an integer additive set-labeling such that the induced function f+:E(G) → P(ℕ0) defined by f+ (uv) = f(u)+ f(v) is also injective. In this paper, we extend the concepts of set-sequential labeling to integer additive set-labelings of graphs and provide some results on them.