Two types of size Ramsey numbers for matchings of small order

For simple graphs G and H, their size Ramsey number is the smallest possible of F such that for any red-blue coloring its edges, contains either a red or blue H. Similarly, we can define connected by adding prerequisite must be connected. In this paper, explore relationships between these numbers give some results on values certain classes graphs. We are mainly interested in cases where 2K2 3K2, H cycle Cn union paths nPm. Additionally, improve an upper bound regarding t m.