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- 저자 : M. S. Subramanya (검색결과 5 건)
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Switching Invariant Neighborhood Signed Graphs
R. Rangarajan,M. S. Subramanya,P. S. K. Reddy 장전수학회 2011 Proceedings of the Jangjeon mathematical society Vol.14 No.2
A signed graph (marked graph) is an ordered pair S = (G, ) (S = (G, μ)),where G = (V,E) is a graph called the underlying graph of S and [수식] is a function. The neighborhood graph of a graph G = (V,E), denoted by N(G),is a graph on the same vertex set V , where two vertices in N(G) are adjacent if, and only if, they have a common neighbor. Analogously, one can define the neighborhood signed graph N(S) of a signed graph [수식] as a signed graph,[수식] where N(G) is the underlying graph of N(S), and for any edge e = uv in N(S),[수식] where for any v 2 V , μ(v) =Y u)μ(v), where for any v 2 V , μ(v) = u2N(v) (uv). In this paper, we characterize signed graphs S for which S N(S), Sc N(S) and N(S) J(S), where J(S) and Sc denotes jump signed graph and complement of signed graph of S respectively.
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(4, d)-Sigraph and Its Applications
Sampathkumar,M. S. Subramanya,P. Siva Kota Reddy 장전수학회 2010 Advanced Studies in Contemporary Mathematics Vol.20 No.1
Let G = (V,E) be a graph. By directional labeling (or d-labeling) of an edge x = uv of G by an ordered 4-tuple (a1, a2, a3, a4), we mean a labeling of the edge x such that we consider the label on uv as (a1, a2, a3, a4) in the direction from u to v, and the label on x as (a4, a3, a2, a1) in the direction from v to u. In this paper, we study graphs, called (4, d)-sigraphs, in which every edge is d-labeled by a 4-tuple (a1, a2, a3, a4), where ak 2 {+, −},for 1 ≤ k ≤ 4. Giving a motivation to study such graphs, we obtain some results by introducing new notions of balance and special types of complementations.
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E. Sampathkumar,P. S. K. Reddy,M. S. Subramanya 장전수학회 2008 Proceedings of the Jangjeon mathematical society Vol.11 No.1
An n-tuple (a₁, a₂, ..., an) is symmetric, if ak = an−k+₁, 1 ≤ k ≤ n. A symmetric n-sigraph (symmetric n-marked graph) is an ordered pair Sn = (G, δ) (Sn = (G, μ)), where G = (V,E) is a graph called the underlying graph of Sn and δ : E → Hn (μ : V → Hn) is a function. Analogous to the concept of Jump sigraph of a sigraph, we define Jump symmetric n-sigraph of a symmetric n-sigraph. Introducing two notions of balance in symmetric n-sigraphs and some notions of complements we characterize the symmetric n-sigraphs which are switching equivalent to their Jump symmetric n-sigraphs.
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(3,d)-sigraph and its applications
E. Sampathkumar,P. S. K. Reddy,M. S. Subramanya 장전수학회 2008 Advanced Studies in Contemporary Mathematics Vol.17 No.1
LetG = (V;E) be a graph and x = uv be an edge in G. By directional labeling (or d-labeling) of an edge x = uv of G by an ordered triple(a1;a2;a3), we mean a labeling of x such that we consider the label on x as (a1;a2;a3) in the direction from u to v, and the label on x as (a3;a2;a1)in the direction from v to u. In this paper, we study graphs in which every edge is d-labeled by a triple (a1;a2;a3), where ak 2 f+ ;g , for 1 k 3,called (3, d)-sigraphs. Giving some motivation to study such graphs, we obtain some results by introducing some notions of balance and special types of complements.
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Switching equivalence in symmetric -sigraphs
R. Rangarajan,P. Siva Kota Reddy,M. S. Subramanya 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.18 No.1
An n-tuple (a1, a2, ..., an) is symmetric, if ak = an−k+1, 1 ≤ k≤ n. A symmetric n-sigraph (symmetric n-marked graph) is an ordered pair Sn = (G, б) (Sn = (G, μ)), where G = (V,E) is a graph called the underlying graph of Sn and [수식] : E → Hn (μ : V → Hn) is a function. Analogous to the concept of the common-edge sigraph of a sigraph, common-edge symmetric n-sigraph of a symmetric n-sigraph is defined. Further, we obtain some switching equivalent characterizations between common-edge symmetric n-sigraph, line symmetric n-sigraph and jump symmetric n-sigraph.
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