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On Edge-balance Index Sets of N cycles Three Nested Graph (n = 0, 1, 2 (mod6))
Ying Wang,Yuge Zheng,C. ADIGA,Shrikanth A S 장전수학회 2011 Advanced Studies in Contemporary Mathematics Vol.21 No.1
Let G be a simple graph with vertex set V (G) and edge set E(G), and let Z_2 ={0, 1}. For a given binary labeling f : E(G) → Z_2, the edge labeling f induces a partial vertex labeling f^* : V (G) → Z_2 such that f^*(v) = 1(0) iff the number of 1-edges(0-edges) is strictly greater than the number of 0-edges(1-edges) incident to v, otherwise f^*(v) is not de¯ned. For i ∈ Z_2, let vf (i) = v(i) = card{v ∈V (G) : f^*(v) = i} and ef (i) = e(i) = card{e ∈ E(G) : f(e) = i}. The edge-balance index set of the graph G, EBI(G), is de¯ned as {|vf (0)-vf (1)| :the edge labeling f is edge-friendlyg. The graph C_n × P_3 is said that three cycles are linked with n paths. In this paper,we will research a structural method of the edge-balance index set of n cycles three nested graph (n≡0, 1, 2(mod6)).
ON THE SKEW ENERGY OF SOME UNITARY CAYLEY DIGRAPHS
C. Adiga,H.N. Ramaswamy,D.D. Somashekara,Z. Khoshbakht 장전수학회 2010 Advanced Studies in Contemporary Mathematics Vol.20 No.2
In this paper we introduce Cayley digraph Dn, n > 1. We show that when n = 3(mod 4) the skew eigenvalues of Dn are the Gauss sums associated with the quadratic character and we also compute its skew energy.
Some normal edge-transitive Cayley graphs on Frobenius groups F_(p, 3)
C. Adiga,A. A. Talebi,H. Ariamanesh 장전수학회 2012 Advanced Studies in Contemporary Mathematics Vol.22 No.3
Let G be a finite group and S a subset of G such that S = S^−1and 1_G ∈/ S. Then the Cayley graph Γ = Cay(G, S) relative to S is the graph with vertex set G and edge set E(Γ(G, S)) = {gh | hg^−1 ∈ S}. Since S is inverse closed and does not contain the identity, this graph is undirected and has no loops. A Cayley graph of a finite group G is called normal edge-transitive,if its automorphism group has a subgroup which both normalizes G and acts transitively on edges. In this paper we determine some normal edge-transitive Cayley Graphs on Frobenius Groups F_p,3, where p is a prime and 3 | p − 1.
On colorings of strongly multiplicative and strongly quotient graphs
C. Adiga,R .K. Zaferani 장전수학회 2006 Advanced Studies in Contemporary Mathematics Vol.13 No.2
Computations of the chromatic number Â(G), the clique number !(G), the cardinality of maximal independent set (G) and the cardinality of minimum de¯ning set d(G; Â) for general graph is difficult. In this paper, we obtain two upper bounds and a lower bound for Â(G) where G is a strongly multiplicative graph of order n. If G is a strongly quotient graph of order n, we provide a lower bound for Â(G), and establish that !(G) = 1+¼(n):We also determine the size of a maximal independent set and minimum defining set of a strongly quotient graph of order n.
A note on Mycielskian type of a graph
C. Adiga,A. Bayad,A. S. Shrikanth 장전수학회 2012 Advanced Studies in Contemporary Mathematics Vol.22 No.1
In this paper we introduce and study an interesting graph transformation which we call the Mycielskian type graph of a graph. We show that MT(G), the Mycielskian type graph of a graph G has no k-fall coloring for any k >= 2. We also compute the spectrum of Mycielskian type graph of a k-regular graph G. Friendly index sets of Mycielskian type graphs of Pn and Cn are determined.
ON STRONGLY SUM DIFFERENCE QUOTIENT GRAPHS
C. Adiga,C. S. S. Swamy 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.19 No.1
In this paper, we introduce the concept of strongly sum difference quotient (SSDQ) graph and show that much studied families of graphs such as cycles, flowers, wheels are SSDQ graphs. We give an upper bound for α(n), the maximum number of edges in a SSDQ graph of order n. Also we derive an explicit formula for α(n) in terms of Eulers phi function.
ON THE SERIES EXPANSION OF THE RAMANUJAN'S CONTINUED FRACTION OF ORDER SIX
C. ADIGA,A. Vanitha,M. S. Surekha 장전수학회 2015 Proceedings of the Jangjeon mathematical society Vol.18 No.3
We give 3- and 6-dissections of Ramanujan's continued fraction of order six and its reciprocal. We also give combinatorial interpretations of the coefficients in the series expansions of the Ramanujan's continued fraction of order six and its reciprocal. These combinatorial results enable us to determine the signs of the coefficients.
Upper bounds for energy of a graph
C. Adiga,R.K. Zaferani 장전수학회 2008 Advanced Studies in Contemporary Mathematics Vol.16 No.2
The energy of a graph G is defined as the sum of absolute values of theeigenvalues of the graph G and is denoted by E(G). In this paper we obtaintwo eigenvalues of a strongly quotient graph SQG with n vertices and maximum number of edges and use them to establish an upper bound for energyof SQG.
Fibonacci Graph and its Energies
Chandrashekar Adiga,Anitha N.,Savitha H. C. 장전수학회 2021 Advanced Studies in Contemporary Mathematics Vol.31 No.1
The energy of a graph is dened as the sum of absolute values of its eigenvalues. In this paper, we compute the spectrum and energy of the Fibonacci graph. Numerous matrices can be associated with a graph and their spectrums provide useful information about the graph. In recent times, various other graph energies are studied, based on eigenvalues of several graph matrices. In the present paper, we also establish relationship between the usual energy of the Fibonacci graph and other energies like Signless Lapalcian energy, Randic energy, maximum degree energy, common-neighborhood energy, 2-distance energy and Seidal energy.