Seminário de Combinatória – Carlos Rodriguez Palma (Universidad Industrial de Santander – Bucaramanga, Colômbia) – 30/04/25 – 14h
O Seminário de Combinatória continua as suas atividades de forma online. Agradecemos a oportunidade de receber ao Professor Carlos Rodriguez Palma da Universidad Industrial de Santander (Bucaramanga – Colombia)
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Data: 30/04/2025
Horário: 2:00pm (Brasil)
Sala: https://meet.google.com/cde-osms-aqn
Palestrante: Carlos Rodriguez Palma – Universidad Industrial de Santander
Título: TNDI Colorings by Sums on Generalized Sierpiński Graphs: Exact Values, Conjectures, and Group Actions
Resumo: This talk focuses on a special type of graph coloring known as total-neighbor-distinguishing coloring by sums. In this setting, adjacent vertices must be distinguished by the total sum of colors assigned to them and their incident edges. We investigate this coloring within the framework of generalized Sierpiński graphs, a family of recursively defined graphs with rich combinatorial structure.
More precisely, we consider the class of graphs S(n, G), constructed from a base graph G, and prove that they satisfy the TNDI-sum conjecture when G is a complete graph, a cycle, or a bipartite graph. In several cases, we determine the exact value of TNDI-sum and observe that it coincides with the chromatic number of the adjacent-vertex-distinguishing total coloring (AVDTC).
In addition to confirming known conjectures in this context, we emphasize the role of group actions as powerful tools for constructing and analyzing such colorings on generalized Sierpiński graphs.
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