On the AVDTC of Sierpiński-type graphs☆

The Adjacent-Vertex-Distinguishing Total Coloring (AVDTC) conjecture asserts that every simple graph can be colored with an AVDTC using at most increment + 3 colors. We show that this conjecture is satisfied for all the Sierpinski graphs Spn, their regularizations +Spn and ++Spn and the fractals obtained as limit space of these graphs. Moreover, we construct explicit total colorings (with at most increment + 2 colors) for Sierpinski triangles graphs STpn and Sierpinski triangle fractal with the limit space STp infinity, for p is an element of {3, 4, 5, 6}, and prove that the AVDTC conjecture is also valid for these cases. (c) 2023 Elsevier B.V. All rights reserved.