Graph polynomials serve as robust algebraic encodings of the intricate combinatorial properties inherent to graphs. At the heart of this discipline lies the Tutte polynomial, an invariant that not ...

Graphs, visual representations outlining the relationships between different entities, concepts or variables, can be very ...

A study by Professor Yinhua Huang’s team at China Agricultural University has for the first time constructed a “graph-based pan-genome” for chickens, ...

Mathematics at Scientific High School for the 2025 Final Exam. The second test of the 2025 final exam at the scientific high ...

This is the first book to comprehensively cover chromatic polynomials of graphs. It includes most of the known results and unsolved problems in the area of chromatic polynomials. Dividing the book ...

Syllabus: The NTA has put the official JEE Main 2026 Syllabus online on their website: jeemain.nta.nic.in. If you're planning ...

This was by far the easiest exhaustive lists to run. It basically counts the edges on each graph and finds the minimum, average and maximum degrees within the graph. Using the Handshake Lemma the ...

Reality is reality and fantasy is fantasy. Pretending fantasy is reality only works insofar as others are willing to tolerate ...

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This repository is a collection of reference implementations for the Model Context Protocol (MCP), as well as references to community built servers and additional resources. The servers in this ...

Abstract We find families of prime diagrams of knots with arbitrary extreme coefficients in their Jones polynomials. Some graph theory is presents in connection with this problem, generalizing ideas ...