• Journal of applied mathematics & informatics
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• 제32권1_2호
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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.

• Journal of applied mathematics & informatics
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• 제42권1호
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• pp.77-83
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• 2024

Chung defined a pebbling move on a graph G as the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The monophonic pebbling number guarantees that a pebble can be shifted in the chordless and the longest path possible if there are any hurdles in the process of the supply chain. For a connected graph G a monophonic path between any two vertices x and y contains no chords. The monophonic pebbling number, µ(G), is the least positive integer n such that for any distribution of µ(G) pebbles it is possible to move on G allowing one pebble to be carried to any specified but arbitrary vertex using monophonic a path by a sequence of pebbling operations. The aim of this study is to find out the monophonic pebbling numbers of the sun graphs, (C_n × P₂) + K₁ graph, the spherical graph, the anti-prism graphs, and an n-crossed prism graph.

• 한국방송∙미디어공학회:학술대회논문집
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• 한국방송공학회 2012년도 하계학술대회
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• pp.164-166
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• 2012

In this paper, we proposed a method for extracting predominant melody of polyphonic music based on harmonic structure. Harmonic structure is an important feature parameter of monophonic signal that has spectral peaks at the integer multiples of its fundamental frequency. We extract all fundamental frequency candidates contained in the polyphonic signal by verifying the required condition of harmonic structure. Then, we combine those harmonic peaks corresponding to each extracted fundamental frequency and assign a rank to each after calculating its harmonic average energy. We run pitch tracking based on the rank of extracted fundamental frequency and continuity of fundamental frequency, and determine the predominant melody. For the query by singing/humming (QbSH) task, we proposed Dynamic Time Warping (DTW) based matching engine. Our system reduces false alarm by combining the distances of multiple DTW processes. To improve the performance, we introduced the asymmetric sense, pitch level compensation, and distance intransitiveness to DTW algorithm.