• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.255-266
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• 2014

For a connected graph G = (V,E) of order at least two, a set S of vertices of G is a monophonic set of G if each vertex v of G lies on an x - y monophonic path for some elements x and y in S. The minimum cardinality of a monophonic set of G is the monophonic number of G, denoted by m(G). Certain general properties satisfied by the monophonic sets are studied. Graphs G of order p with m(G) = 2 or p or p - 1 are characterized. For every pair a, b of positive integers with $2{\leq}a{\leq}b$, there is a connected graph G with m(G) = a and g(G) = b, where g(G) is the geodetic number of G. Also we study how the monophonic number of a graph is affected when pendant edges are added to the graph.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.2
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• pp.445-451
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• 2010

This paper presents a threshold adaptation based voice query transcription scheme for music information retrieval. The proposed scheme analyzes monophonic voice signal and generates its transcription for diverse music retrieval applications. For accurate transcription, we propose several advanced features including (i) Energetic Feature eXtractor (EFX) for onset, peak, and transient area detection; (ii) Modified Windowed Average Energy (MWAE) for defining multiple small but coherent windows with local threshold values as offset detector; and finally (iii) Circular Average Magnitude Difference Function (CAMDF) for accurate acquisition of fundamental frequency (F0) of each frame. In order to evaluate the performance of our proposed scheme, we implemented a prototype music transcription system called AMT2 (Automatic Music Transcriber version 2) and carried out various experiments. In the experiment, we used QBSH corpus [1], adapted in MIREX 2006 contest data set. Experimental result shows that our proposed scheme can improve the transcription performance.