• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.873-893
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• 2023

In 2017, Nikiforov proposed the A_𝛼-matrix of a graph G. This novel matrix is defined as A_𝛼(G) = 𝛼D(G) + (1 - 𝛼)A(G), 𝛼 ∈ [0, 1], where D(G) and A(G) are the degree diagonal matrix and adjacency matrix of G, respectively. Recently, Zhai, Xue and Liu [39] considered the Brualdi-Hoffman-type problem for Q-spectra of graphs with given matching number. As a continuance of it, in this contribution we consider the Brualdi-Hoffman-type problem for A_𝛼-spectra of graphs with given matching number. We identify the graphs with given size and matching number having the largest A_𝛼-spectral radius for ${\alpha}{\in}[{\frac{1}{2}},1)$.

• Journal of the Korean earth science society
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• v.38 no.1
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• pp.1-10
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• 2017

The symbiotic star AG Peg is a nebulous binary system that consists of giant star (GS) and white dwarf (WD). We investigated the HI Balmer emission lines of the symbiotic nova AG Peg, observed in 1998, 2001, and 2002 at Lick Observatory. The $H{\alpha}$ and $H{\beta}$ line profiles consist of blue-shifted, red-shifted, and broad components of which intensities and width showed notable changes. The HI emission line profiles that represent the kinematics of the gaseous nebula appear to be mainly from an accretion disk in relatively large radius from the WD. Considering the line of an observer's sight, both GS and WD are located at the sky plane side by side during the 1998 observation, while the WD is in front of GS during 2002 but the WD in rear during 2001. Such a relative position and the spectral line intensity variation imply that a fairly constant outflow occurs into WD from GS which caused to maintain the rotating thick accretion disk structure responsible for the observed spectral lines.