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The Line n-sigraph of a Symmetric n-sigraph-V
Reddy, P. Siva Kota,Nagaraja, K.M.,Geetha, M.C. Department of Mathematics 2014 Kyungpook mathematical journal Vol.54 No.1
An n-tuple ($a_1,a_2,{\ldots},a_n$) is symmetric, if $a_k$ = $a_{n-k+1}$, $1{\leq}k{\leq}n$. Let $H_n$ = {$(a_1,a_2,{\ldots},a_n)$ ; $a_k$ ${\in}$ {+,-}, $a_k$ = $a_{n-k+1}$, $1{\leq}k{\leq}n$} be the set of all symmetric n-tuples. A symmetric n-sigraph (symmetric n-marked graph) is an ordered pair $S_n$ = (G,${\sigma}$) ($S_n$ = (G,${\mu}$)), where G = (V,E) is a graph called the underlying graph of $S_n$ and ${\sigma}$:E ${\rightarrow}H_n({\mu}:V{\rightarrow}H_n)$ is a function. The restricted super line graph of index r of a graph G, denoted by $\mathcal{R}\mathcal{L}_r$(G). The vertices of $\mathcal{R}\mathcal{L}_r$(G) are the r-subsets of E(G) and two vertices P = ${p_1,p_2,{\ldots},p_r}$ and Q = ${q_1,q_2,{\ldots},q_r}$ are adjacent if there exists exactly one pair of edges, say $p_i$ and $q_j$, where $1{\leq}i$, $j{\leq}r$, 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 $S_n$ = (G,${\sigma}$) as a symmetric n-sigraph $\mathcal{R}\mathcal{L}_r$($S_n$) = ($\mathcal{R}\mathcal{L}_r(G)$, ${\sigma}$'), where $\mathcal{R}\mathcal{L}_r(G)$ is the underlying graph of $\mathcal{R}\mathcal{L}_r(S_n)$, where for any edge PQ in $\mathcal{R}\mathcal{L}_r(S_n)$, ${\sigma}^{\prime}(PQ)$=${\sigma}(P){\sigma}(Q)$. It is shown that for any symmetric n-sigraph $S_n$, its $\mathcal{R}\mathcal{L}_r(S_n)$ is i-balanced and we offer a structural characterization of super line symmetric n-sigraphs of index r. Further, we characterize symmetric n-sigraphs $S_n$ for which $\mathcal{R}\mathcal{L}_r(S_n)$~$\mathcal{L}_r(S_n)$ and $$\mathcal{R}\mathcal{L}_r(S_n){\sim_=}\mathcal{L}_r(S_n)$$, where ~ and $$\sim_=$$ denotes switching equivalence and isomorphism and $\mathcal{R}\mathcal{L}_r(S_n)$ and $\mathcal{L}_r(S_n)$ are denotes the restricted super line symmetric n-sigraph of index r and super line symmetric n-sigraph of index r of $S_n$ respectively.
P. Siva Kota Reddy,B. Prashanth,T. R. Vasanth Kumar 장전수학회 2011 Advanced Studies in Contemporary Mathematics Vol.21 No.4
In this paper, we define the antipodal signed digraph A(D) of a given signed digraph S = (D, σ) and offer a structural characterization of antipodal signed digraphs.Further, we characterize signed digraphs S for which S ~ A(S) and S ~ A (S) where denotes switching equivalence and A (S) and S are denotes the antipodal signed digraph and complementary signed digraph of S respectively.
The Line n-Sigraph of a Symmetric n-Sigraph-II
P. Siva Kota Reddy,V. Lokesha,Gurunath Rao Vaidya 장전수학회 2010 Proceedings of the Jangjeon mathematical society Vol.13 No.3
An n-tuple (a1, a2, ..., an) is symmetric, if ak = an-k+1, 1 ≤ k ≤ n. Let Hn = {(a1, a2, ..., an) : ak ∈ {+, -}, ak = an-k+1, 1 ≤ k ≤ n} be the set of all symmetric n-tuples. A symmetric n-sigraph (symmetric n-marked graph) is an ordered pair Sn = (G, σ) (Sn = (G, μ)), where G = (V, E) is a graph called the underlying graph of Sn and σ : E → Hn (μ : V → Hn) is a function. Given a connected graph H of order at least 3, the H-Line Graph of a graph G = (V, E), denoted by HL(G), is a graph with the vertex set E, the edge set of G where two vertices in HL(G) are adjacent if, and only if, the corresponding edges are adjacent in G and there exists a copy of H in G containing them. Analogously, for a connected graph H of order at lest 3, we define the H-Line symmetric n-sigraph HL(Sn) of a symmetric n-sigraph Sn = (G, σ) as a symmetric n-sigraph, HL(Sn) = (HL(G), σ'),and for any edge e1e2 in HL(Sn), σ'(e1e2) = σ(e1)σ(e2). In this paper,we characterize symmetric n-sigraphs Sn which are H-line symmetric n-sigraphs and study some properties of H-line graphs as well as H-line symmetric n-sigraphs. The notion HL(Sn) which generalizes the notion of line symmetric n-sigraph L(Sn) introduced by E. Sampathkumar et al. (2010).
P. Siva Kota Reddy,U. K. Misra 장전수학회 2013 Advanced Studies in Contemporary Mathematics Vol.23 No.3
In this paper, we dene the graphoidal signed graph of a given signed graph and oer a structural characterization of graphoidal signed graphs. In the sequel, we also obtained some switching equivalence characteriza-tions.
INVERSE SUM INDEG ENERGY OF A GRAPH
P. SIVA KOTA REDDY,K. N. PRAKASHA,Ismail Naci CANGUL 장전수학회 2021 Advanced Studies in Contemporary Mathematics Vol.31 No.1
Let G be a graph with n vertices and let di denote the degree of the vertex vi. For a given graph, there are more than 100 ma- trices obtained by using some properties of the graph. Most important and used ones are the adjacency, incidency and Laplacian matrices. Re- cently, several graph topological indices have been used in dening new graph matrices. Graph energy is the quantity obtained as the sum of the absolute values of all eigenvalues of the adjacency matrix corresponding to the graph. Several types of energy have been dened and applied in dierent applications by means of such graph matrices in place of the adjacency matrix. The inverse sum indeg matrix of a graph G is the n n matrix whose (i; j)-th entry is equal to didj di+dj if the ith and the jth vertices are adjacent and 0 otherwise. The inverse sum indeg energy ISIE(G) of G is similarly dened as the sum of the absolute values of the eigenvalues of the inverse sum indeg matrix. In this paper, we compute the inverse sum indeg characteristic polynomial and the inverse sum indeg energy for standard graphs. Some properties and bounds for ISIE(G) are also obtained.
Inequalities among means of two positive arguments in index (conjugate index) sets
P. Siva Kota Reddy,K. M. Nagaraja,K. Sridevi 장전수학회 2023 Proceedings of the Jangjeon mathematical society Vol.26 No.2
Inequalities among means of two positive arguments in index (conjugate index) sets
Slant sub-manifolds of generalized Sasakian-space-forms
G. SOMASHEKHARA,P. SIVA KOTA REDDY,K. SHIVASHANKARA,N. PAVANI 장전수학회 2022 Proceedings of the Jangjeon mathematical society Vol.25 No.1
In this paper, we study the slant submanifolds of general- ized Sasakian space forms when structure tensor field ∅ is Killing. Also, obtained the conditions for anti-invariant submanifolds under some ge- ometrical conditions such as ∇Q = 0 and ∇T = 0.
Squares stress sum index for graphs
R. Rajendra,P. SIVA KOTA REDDY,C. N. HARSHAVARDHANA,Khaled A. A. Alloush 장전수학회 2023 Proceedings of the Jangjeon mathematical society Vol.26 No.4
Squares stress sum index for graphs
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.
Set-prime graph of a finite group
R. RAJENDRA,P.Siva Kota Reddy,K. V. Madhusudhan 장전수학회 2019 Proceedings of the Jangjeon mathematical society Vol.22 No.3
Let S be a non-empty set of positive integers. We dene the set-prime graph GS( ) of a given nite group of order n with respect to S, as a graph with vertex set V (GS( )) = and any two vertices a and b are adjacent in GS( ) if and only if (o(a); o(b)) 2 S. In this paper, we observe that order prime and general order prime graphs are special cases of set-prime graphs and we investigate some properties of set-prime graphs of nite groups.