In this paper, we discuss some graphs whose incidence-adjacent vertex distinguishing total chromatic number is just ¿, ¿ + 1, ¿ + 2, and present a conjecture that the incidence-adjacent vertex ...

This method takes two lists as input: sources and destinations. Each pair (sources [i], destinations [i]) represents a directed edge from a vertex with data sources [i] to a vertex with data ...

Concurrently, research on total perfect codes in Cayley graphs has elucidated how conjugation-closed subsets of groups can yield comprehensive vertex coverings, thus ensuring that every vertex is ...

Let G (V, E) be a simple graph, k is a positive integer, f is a mapping from V (G) ¿ E (G) to {1, 2, ..., k} such that ¿uv ¿ E (G), then f (u) ¿ f (v); ¿uv,vw ¿ E (G), u ¿ w,f (uv) ¿ f (vw); ¿uv ¿ E ...