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Chandrashekar Adiga,E. Sampathkumar,M. A. Sriraj,Shrikanth A S 장전수학회 2013 Proceedings of the Jangjeon mathematical society Vol.16 No.3
In this paper, we introduce the concept of color energy of a graph, Ec(G) andcompute the color energy Ex(G) of few families of graphs with minimum number ofcolors. It depends on the underlying graph and colors on its vertices. We establishan upper bound and a lower bound for color energy. Also we introduce the conceptof complement of a colored graph and compute energies of complement of coloredgraphs of few families of graphs.
Arithmetic properties of partition four tuples with 3-cores
Chandrashekar Adiga,Ranganatha D 장전수학회 2016 Advanced Studies in Contemporary Mathematics Vol.26 No.3
Let A<sup>k<sub>3 (n) denote the number of partition k-tuples of n where each partition is 3- core. In this paper, employing elementary generating function dissection techniques, we establish several innite families of congruences for A<sup>4<sub>3 (n). For example, we proved that for all integers α ≥ 0, k ≥ 0 and n ≥ 0, A<sup>4<sub>3(4<sup>(k+1)n + 5.2<sup>(2k+1) - 4/ 3)≡ 0 mod (4<sup>4k+5 -4)/63), A<sup>4<sub>3(16<sup(k+1)α n + 4<sup>(2k+2)α+1 -4) / 3 ≡ A<sup>4<sub>3(n) mod (64<sup>k+1 -1/63).
Spectra of F-sum graphs and F-product graphs
Chandrashekar Adiga,Rakshith B. R. 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.2
Several graph operations based on subdivision graph and its variants have been introduced by many researchers and their spectral properties have been studied. The F-sum graphs and F-product graphs are one among these graph operations. In literature, many topological indices of F-sum graphs and F-product graphs have been examined. In this paper, we rst introduce two matrix forms named as F-sum matrix and F-product matrix and describe their spectra, and then using the spectra of these matrices, we compute the spectra of F-sum graphs and F-product graphs.
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.