a2, ..., an) , where G = (V, E) is a graph called the underlying graph of Sn and σ : E → Hn (µ : V → Hn) is a function. The restricted super line graph of index r of a graph G, denoted by RLr(G). The vertices of RLr(G) are the r-subsets of E(G) and two vertices P = {p1, p2, ..., pr} and Q = {q1, q2, ..., qr} are adjacent if there exists exactly one pair of edges, say pi and qj, where 1 ≤ i, j ≤ r, that are adjacent edges in G. Analogously, one can define the restricted super line symmetric n-sigraph of index r of a symmetric n-sigraph Sn = (G, σ) as a symmetric n-sigraph RLr(Sn) = (RLr(G), σ ′ ), where RLr(G) is the underlying graph of RLr(Sn), where for any edge P Q in RLr(Sn), σ ′ (P Q) = σ(P )σ(Q). It is shown that for any symmetric n-sigraph Sn, its RLr(Sn) is i-balanced and we offer a structural characterization of super line symmetric n-sigraphs of index r. Further, we characterize symmetric n-sigraphs Sn for which RLr(Sn) ∼ Lr(Sn) and RLr(Sn) ∼ = Lr(Sn), where ∼ and ∼ = denotes switching equivalence and isomorphism and RLr(Sn) and Lr(Sn) are denotes the restricted super line symmetric n-sigraph of index r and super line symmetric n-sigraph of index r of Sn respectively.
In this paper, we define the edge C k signed graph of a given signed graph and shown that for any signed graph Σ, its edge C k signed graph E k (Σ) is balanced. We then give structural characterization of edge C k signed graphs. Further, we obtain a structural characterization of signed graphs that are switching equivalent to their the edge C k signed graphs.
Abstract.In this paper, we define the homogeneous functions Gn µ,r (a, b) and
gnµ,r(a, b).Further we study properties, relations with means, applications to inequalities and partial derivatives. We also give some applications of these means related toFarey fractions and Ky Fan type inequalities.
In this paper the Centroidal mean labeling of cycle containing graphs such as Triangular Ladder T L n , cycle C n , Polygonal chain G mn , Square graph P 2 n , L n K 1,2 , Ladder L n are found.
Abstract. In the recent years, the Schur convexity and Schur geometrically convexity of Stolarsky's mean values have grabed the focus of many mathematicians and researchers. In this article, the Schur convexity of Stolarsky's extended type mean values are discussed.Mathematics subject classification (2010): Primary 26D10, 26D15.
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