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TRULY NONTRIVIAL GRAPHOIDAL COVERS-I
PURNIMA GUPTA,RAJESH SINGH 장전수학회 2017 Proceedings of the Jangjeon mathematical society Vol.20 No.4
A graphoidal cover of a graph G is a collection Ψ of non- trivial paths (not necessarily open) in G such that every vertex of G is an internal vertex of at most one path in Ψ and every edge of G is in exactly one path in Ψ. A graphoidal cover Ψ of G is a truly non- trivial graphoidal cover (TNT graphoidal cover) of G if every path in Ψ has length greater than 1. A graph G is a truly nontrivial graph (TNT graph) if it possesses a TNT graphoidal cover. In this paper we intend to answer the fundamental question "Does every graph possess a TNT graphoidal cover ?", raised by Fred Roberts in first author's thesis re- port. After exhibiting the fact that not every graph possesses a TNT graphoidal cover, we could obtain some forbidden structures for a graph to be a TNT graph. And in the quest to find graphs having a TNT graphoidal cover, we could identify certain classes of trees and unicyclic graphs which are TNT graphs.
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Purnima Chopra,Mamta Gupta,Kanak Modi Korean Mathematical Society 2023 대한수학회논문집 Vol.38 No.3
Our aim is to establish certain image formulas of the (p, q)-extended modified Bessel function of the second kind M<sub>ν,p,q</sub>(z) by employing the Marichev-Saigo-Maeda fractional calculus (integral and differential) operators including their composition formulas and using certain integral transforms involving (p, q)-extended modified Bessel function of the second kind M<sub>ν,p,q</sub>(z). Corresponding assertions for the Saigo's, Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, q)-extended modified Bessel function of the second kind M<sub>ν,p,q</sub>(z) and Fox-Wright function <sub>r</sub>Ψ<sub>s</sub>(z).
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Chopra, Purnima,Gupta, Mamta,Modi, Kanak Korean Mathematical Society 2022 대한수학회논문집 Vol.37 No.4
Our aim is to establish certain image formulas of the (p, 𝜈)-extended Gauss' hypergeometric function F<sub>p,𝜈</sub>(a, b; c; z) by using Saigo's hypergeometric fractional calculus (integral and differential) operators. Corresponding assertions for the classical Riemann-Liouville(R-L) and Erdélyi-Kober(E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, 𝜈)-extended Gauss's hypergeometric function F<sub>p,𝜈</sub>(a, b; c; z) and Fox-Wright function <sub>r</sub>Ψ<sub>s</sub>(z). We also established Jacobi and its particular assertions for the Gegenbauer and Legendre transforms of the (p, 𝜈)-extended Gauss' hypergeometric function F<sub>p,𝜈</sub>(a, b; c; z).
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