On Uniform Linear Hypergraph Set-indexers of a Graph
نویسنده
چکیده
For a graph G = (V,E) and a non-empty set X, a linear hypergraph set-indexer (LHSI) is a function f : V (G)→ 2X satisfying the following conditions: (i)f is injective (ii) the ordered pair Hf (G) = (X, f(V )), where f(V ) = {f(v) : v ∈ V (G)}, is a linear hypergraph, (iii) the induced set-valued function f⊕ : E → 2X , defined by f⊕(uv) = f(u)⊕ f(v),∀ uv ∈ E is injective, and (iv) Hf⊕(G) = (X, f⊕(E)), where f⊕(E) = {f⊕(e) : e ∈ E}, is a linear hypergraph. In this paper, we characterize graphs which admit 3-uniform LHSI and establish the relation between the cyclomatic numbers of the given graph, its line graph and the two hypergraphs associated with a 3-uniform LHSI. Also, we determine the upper LHSI number of graph G having 2 ≤ δ(G) ≤ ∆(G) ≤ 3 and girth g(G) ≥ 5.
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تاریخ انتشار 2011