• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.425-441
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• 2014

In this paper, we first present the properties of the graph which maximize the spectral radius among all graphs with prescribed degree sequence. Using these results, we provide a somewhat simpler method to determine the unicyclic graph with maximum spectral radius among all unicyclic graphs with a given degree sequence. Moreover, we determine the bicyclic graph which has maximum spectral radius among all bicyclic graphs with a given degree sequence.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.113-125
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• 2019

In this paper, we introduce the elimination ideal $I_D(G)$ associated to a simple finite graph G. We obtain the upper bound of Castelnuovo-Mumford regularity of elimination ideal for various classes of graphs.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.467-475
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• 2020

Let G be a chemical graph with vertex set {v₁, v₁, …, v_n} and degree sequence d(G) = (deg_G(v₁), deg_G(v₂), …, deg_G(v_n)). The inverse degree, R(G) of G is defined as $R(G)={\sum{_{i=1}^{n}}}\;{\frac{1}{deg_G(v_i)}}$. The cyclomatic number of G is defined as γ = m - n + k, where m, n and k are the number of edges, vertices and components of G, respectively. In this paper, some upper bounds on the diameter of a chemical graph in terms of its inverse degree are given. We also obtain an ordering of connected chemical graphs with respect to the inverse degree.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.533-544
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• 2013

The multiplicative version of Wiener index (${\pi}$-index), proposed by Gutman et al. in 2000, is equal to the product of the distances between all pairs of vertices of a (molecular) graph G. In this paper, we first present some sharp bounds in terms of the order and other graph parameters including the diameter, degree sequence, Zagreb indices, Zagreb coindices, eccentric connectivity index and Merrifield-Simmons index for ${\pi}$-index of general connected graphs and trees, as well as a Nordhaus-Gaddum-type bound for ${\pi}$-index of connected triangle-free graphs. Then we study the behavior of ${\pi}$-index upon the case when removing a vertex or an edge from the underlying graph. Finally, we investigate the extremal properties of ${\pi}$-index within the set of trees and unicyclic graphs.