Saturation Numbers for Linear Forests$$P_5 \cup tP_2$$P5∪tP2

A graph $$G$$G is $$F$$F-saturated if it has no $$F$$F as a subgraph, but does contain $$F$$F after the addition of any new edge. The saturation number, $$sat(n,F)$$sat(n,F), is the minimum number of edges of a graph in the set of all $$F$$F-saturated graphs with order $$n$$n. In this paper, we determine the saturation number $$sat(n,P_5\cup tP_2)$$sat(n,P5∪tP2) for $$n\ge 3t+8$$n≥3t+8 and characterize the extremal graphs for $$n>(18t+76)/5$$n>(18t+76)/5.

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