Ranking numbers of graphs

Rank numbers for some trees and unicyclic graphs

“…An explicit formula for the rank number of a caterpillar was determined by Chang et al [4]. We present an analogous result here for caterpillar cycles.…”

“…However, rank numbers have been determined for several families of graphs including: paths, cycles, split graphs, complete multipartite graphs, Möbius ladder graphs, caterpillars, powers of paths and cycles, and some grid graphs [1][2][3][4][6][7][8]12], and [13]. A problem of interest is determining the rank number of a tree.…”

“…The rank number of a caterpillar was determined by Chang et al [4]. Here we consider the rank number of a cycle with pendant edges, which we will call a caterpillar cycle.…”

Rank numbers of grid graphs

“…, v n . Recently, Chang et al [3] and Ortiz et al [21] independently found the rank number of the prism. The computation of rank number of the prism is included here for comparison with that of the Möbius ladder.…”

“…Although an early version of the present paper included the formulas χ r (P k n ) = k + χ r (P k  n−k 2  ) and χ r (C k n ) = k + χ r (P k n−k ), we omit the proofs here because they were independently found by Chang et al and appeared in [3].…”