2014•Unpublished venueOpen access
Total Minimal Dominating Signed Graph
P. Siva Kota Reddy, Sandip Vijay
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Abstract
Abstract: A Smarandachely k-signed graph (Smarandachely k-marked graph) is an ordered pair S = (G,σ) (S = (G,µ)) where G = (V, E) is a graph called underlying graph of S and σ: E → (e1, e2,..., ek) (µ: V → (e1, e2,..., ek)) is a function, where each ei ∈ {+,−}. Particularly, a Smarandachely 2-signed graph or Smarandachely 2-marked graph is called abbreviated a signed graph or a marked graph. In this paper, we define the total minimal dominating signed graph Mt(S) = (Mt(G), σ) of a given signed digraph S = (G,σ) and offer a structural characterization of total minimal dominating signed graphs. Further, we characterize signed graphs S for which S ∼ Mt(S) and L(S) ∼ Mt(S), where ∼ denotes switching equivalence and Mt(S) and L(S) are denotes total minimal dominating signed graph and line signed graph of S respectively. Key Words: Smarandachely k-signed graphs, Smarandachely k-marked graphs, signed graphs, marked graphs, balance, switching, total minimal dominating signed graph, line