The field of graph theory is witnessing significant developments in the area of graph connectivity and structure. Researchers are making notable progress in understanding the properties of graphs and developing efficient algorithms to solve complex problems. One of the key directions is the study of fault-tolerant connectivity preservers, which has led to improved bounds and constructions for directed graphs. Additionally, there is a growing interest in understanding the structural parameters of graphs, such as chordality and diameter, and their impact on algorithmic complexity. Noteworthy papers in this area include: Near-Optimal Fault-Tolerant Strong Connectivity Preservers, which nearly closes the gap for directed graphs and improves the state-of-the-art for a closely related object. Finding a HIST: Chordality, Structural Parameters, and Diameter, which provides a comprehensive investigation of the HIST problem from both structural and algorithmic viewpoints. Maximum Biclique for Star 1,2,3 -free and Bounded Bimodularwidth Twin-free Bipartite Graphs, which efficiently solves the maximum biclique problem for two classes of bipartite graphs. Parameterized Complexity of s-Club Cluster Edge Deletion, which resolves the question of whether the problem is FPT when parameterized by treewidth alone and provides FPT algorithms for several parameters.