http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
GENETIC ALGORITHMIC APPROACH TO FIND THE MAXIMUM WEIGHT INDEPENDENT SET OF A GRAPH
Abu Nayeem, Sk. Md.,Pal, Madhumangal 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.25 No.1
In this paper, Genetic Algorithm (GA) is used to find the Maximum Weight Independent Set (MWIS) of a graph. First, MWIS problem is formulated as a 0-1 integer programming optimization problem with linear objective function and a single quadratic constraint. Then GA is implemented with the help of this formulation. Since GA is a heuristic search method, exact solution is not reached in every run. Though the suboptimal solution obtained is very near to the exact one. Computational result comprising an average performance is also presented here.
EXTREMAL F-INDICES FOR BICYCLIC GRAPHS WITH k PENDANT VERTICES
RUHUL AMIN,SK. MD. ABU NAYEEM 한국수학교육학회 2020 純粹 및 應用數學 Vol.27 No.4
Long back in 1972, it was shown that the sum of the squares of vertex degrees and the sum of cubes of vertex degrees of a molecular graph both have large correlations with total π-electron energy of the molecule. Later on, the sum of squares of vertex degrees was named as first Zagreb index and became one of the most studied molecular graph parameter in the field of chemical graph theory. Whereas, the other sum remained almost unnoticed until recently except for a few occasions. Thus it got the name “forgotten” index or F-index. This paper inves- tigates extremal graphs with respect to F-index among the class of bicyclic graphs with n vertices and k pendant vertices, 0≤k≤n − 4. As consequences, we obtain the bicyclic graphs with largest and smallest F-indices.