An L(2, l)-coloring of a graph G is an assignment of labels from {0,1,..., A} to the vertices of G such that vertices at distance two get different labels and adjacent vertices get labels that are at ...

Rahman and Kaykobad introduced a shortest distance based condition for finding the existence of Hamiltonian paths in graphs as follows: Let G be a connected graph with n vertices, and if d (u) + d (v) ...

Abstract The adjacent vertex-distinguishing total chromatic number of a graph 𝐺, denoted by χ𝑎𝑡 (𝐺), is the smallest denoted by 𝑘 for which 𝐺 has a proper total 𝑘-coloring such that any two ...