Manuscript Topics

Graph Theory and Combinatorics represent interconnected pillars of discrete mathematics, jointly exploring the structure, enumeration, and optimization of finite systems. Graph Theory focuses on abstract models of relationships (graphs), composed of vertices (entities) connected by edges (pairwise interactions). Combinatorics concerns the principled counting (enumeration), arrangement, and selection of discrete structures, alongside analyzing their properties and extremal constraints. Together, these fields investigate how combinatorial methods—such as generating functions, probabilistic techniques, and extremal set theory—solve graph problems (e.g., finding optimal network flows, characterizing graph families, or computing graph parameters). Conversely, graphs serve as fundamental combinatorial objects for encoding complex relations in designs, permutations, and optimizations. This symbiotic scope includes topics like graph coloring, extremal graph theory, random graphs, combinatorial designs, network algorithms, and Ramsey theory, unified by the study of discrete, finite configurations and their interactions.

Potential topics include but are not limited to the following:  
• Structural Graph Theory  
• Algebraic Graph Theory  
• Graph Colorings  
• Graph Algorithms  
• Topological Graph Theory  
• Combinatorial Optimization on Graphs  
• Random Graphs  
• Applications of graph theory  
• Cayley graphs  
• Chemical graphs  
• Colored graphs  
• Connectivity  
• Digraphs  
• Distance regular graphs  
• Eigenvalues of graphs  
• Eulerian and Hamiltonian graphs  
• Extremal problems in graphs  
• Flows in graphs  
• Graph algorithms and complexity analysis  
• Graph embedding  
• Graph parameters  
• Graph polynomials  
• Hypergraphs  
• Matching  
• NP-hard problems in graphs  
• Paths and cycles  
• Planar graphs  
• Ramsey problems  
• Turán problems  
• Enumerative Combinatorics  
• Extremal Combinatorics  
• Design Theory  
• Combinatorial Geometry  
• Combinatorial Number Theory  
• Probabilistic Combinatorics

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