Combinatorics and Graph Theory

2608 Submissions

[3] viXra:2608.0061 [pdf] submitted on 2026-08-16 00:17:33

An Operator Calculus and Corrector Theory for Binomial Coecients at Negative Integer Indices

Authors: Ahcene Ait Saadi
Comments: 17 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We study a self-contained combinatorial equality, discovered by the author some forty years ago, which extends [(n, p)^T)]to negative integer indices without invoking any extension of the factorial...
Category: Combinatorics and Graph Theory

[2] viXra:2608.0054 [pdf] submitted on 2026-08-14 20:34:54

Magic Squares of the 4th and 8th Orders Mathematical Projections and Practical Applications

Authors: Andrey V. Voron
Comments: 7 Pages.

The study demonstrates that projecting order-4 and order-8 magic squares onto a tesseract preserves their fundamental numerical invariants. Similarly, the 4×4 Dürer's magic square is projected onto the vertices of an octagonal prism with internal spatial connections. The results obtained in this study open up prospects for utilizing multidimensional geometry to develop new data distribution algorithms. The presented mathematical symmetries can find practical applications in high-tech and theoretical disciplines.
Category: Combinatorics and Graph Theory

[1] viXra:2608.0021 [pdf] submitted on 2026-08-06 15:40:32

Study of Roman Domination Number in Deg Centric Graphs

Authors: Kevin Elijah Valentine
Comments: 14 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Graph theory plays a vital role in the study of mathematical structures and their applicationsin communication networks, optimization, and computer science. Among the variousdomination parameters, the Double Roman Domination Number has attracted significant attentiondue to its enhanced defensive strategy compared with classical domination concepts.This paper investigates the Double Roman Domination Number of Degree-Centric Graphsobtained from several standard graph families. The degree-centric transformation is firstconstructed for each graph, and the corresponding Double Roman Domination Numbers aredetermined. Based on these results, general observations and formulas are established fordifferent classes of graphs, illustrating the relationship between the degree-centric transformationand the domination parameter. The obtained results extend the study of dominationin transformed graphs and provide a foundation for future research in degree-centric graphtheory.
Category: Combinatorics and Graph Theory