%0 Journal Article
%T When Sciences Overlaps: A Matching Game under             a Graph Concept
%A Shahd H. Alkaraz
%J Scientific & Academic Publishing
%D 2020
%R 10.5923/j.ajms.20201002.04
%X Initially, we provide basic knowledge of definitions and concepts related to the concept of matching in the graph. We are studying a model of games based on two players who take turns adding edges to <img src=image/10.5923.j.ajms.20201002.04_001.gif></img> this process eventually produces a maximal matching of the graph. We call the first Maximizer and second player Minimizer. The first aims to get a final matching to be large while the second one wants to reduce it. Maximizer wins if he manages a maximal matching while Minimizer wins if he can prevent him from doing this. The matcher number <img src=image/10.5923.j.ajms.20201002.04_002.gif></img> is the number of edges chosen when both players play optimally, while the matching number <img src=image/10.5923.j.ajms.20201002.04_003.gif></img> is the number of maximum matching edges. In this research we study the relationship between <img src=image/10.5923.j.ajms.20201002.04_004.gif></img> and <img src=image/10.5923.j.ajms.20201002.04_005.gif></img>. And we also prove some results on types of graph
%K Maximal matching
%K Maximum matching
%K Matching
%K Matcher game
%U http://article.sapub.org/10.5923.j.ajms.20201002.04.html