2016/10/01 by P. K. Ashraf, Ashraf, P. K., Germina, K. A. +1
Computer Science · #05C22 #05C78 #Advanced Algebra and Logic #Advanced Graph Theory Research #FOS: Mathematics #General Mathematics (math.GM) #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.1610.00698
openalex publication_date 2016/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a non-empty ground set and P(X) be its power set. A set-labeling (or a set-valuation) of a graph G is an injective set-valued function f:V(G)→ P(X) such that the induced function f^⊕:E(G) → P(X) is defined by f^⊕(uv) = f(u)⊕ f(v), where f(u)⊕ f(v) is the symmetric difference of the sets f(u) and f(v). A graph which admits a set-labeling is known to be a set-labeled graph. A set-labeling f of a graph G is said to be a set-indexer of G if the associated function f^⊕ is also injective. In this paper, we define the notion of set-valuations of signed graphs and discuss certain properties of signed graphs which admits certain types of set-valuations.