Here are Some easy to intermediate codeforces graph and backtracking problems this problems normally only use some basic knowledge of graphs/trees + basic algorithms , I hope it helps

1944A - Destroying Bridges rate : 800 -> basic of graphs [Very Simple]

1598A - Computer Game rate : 800 -> not so much graph [Very Simple]

1797A - Li Hua and Maze rate : 800 -> not so much graph + edge cases [Very Simple]

1843C - Sum in Binary Tree rate : 800 -> not so much graph or tree [Very Simple]

939A - Love Triangle rate : 800 -> can be solved with graph or not [Very Simple]

115A - Party and 116C - Party rate : 900 -> bfs [Simple]

500A - New Year Transportation rate : 1000 -> dfs [Simple]

727A - Transformation: from A to B rate : 1000 -> backtracking / dfs [Simple]

476A - Dreamoon and Stairs rate : 1000 -> backtracking + some optimization [Simple]

1020B - Badge rate : 1000 -> dfs [Simple]

122A - Lucky Division rate : 1000 -> backtracking [Simple]

1324C - Frog Jumps rate : 1100 -> not so much graph but can be solved with dfs [Very Simple]

445A - DZY Loves Chessboard rate : 1200 -> can be solved with dfs [Simple(simpler than it's rating)]

217A - Ice Skating rate : 1200 -> dfs [Simple/Intermediate]

893C - Rumor rate : 1300 -> dfs [Simple]

476B - Dreamoon and WiFi rate : 1300 -> backtracking [Simple]

1638C - Inversion Graph rate : 1300 -> creativity [Simple/Intermediate]

1970C1 - Game on Tree (Easy) rate : 1300 -> trees + dfs/bfs [Simple/Intermediate]

96B - Lucky Numbers (easy) rate : 1300 -> backtracking [Simple]

1143C - Queen rate : 1400 -> trees + you can use dfs/bfs [Simple]

520B - Two Buttons rate : 1400 -> bfs [Simple/Intermediate]

580C - Kefa and Park rate : 1500 -> trees + dfs/bfs [Intermediate]

977E - Cyclic Components rate : 1500 -> dfs [Intermediate]

377A - Maze rate : 1600 -> bfs [Intermediate]

601A - The Two Routes rate : 1600 -> bfs / matrix [Intermediate/Hard]

1363C - Game On Leaves rate : 1600 -> trees / some edge cases only [Simple/Intermediate]

1144F - Graph Without Long Directed Paths rate : 1700 -> bipartite graphs [Intermediate/Hard]

1093D - Beautiful Graph rate : 1700 -> bipartite graphs [Intermediate/Hard]

1970C2 - Game on Tree (Medium) rate : 1700 -> a little hard + dfs/bfs [Intermediate/Hard]