Some problems concerning distance and path degree sequences

On Some Edge Rotation Distance Graphs

“…This was further studied by Bloom et al [25], Halberstam et al [27], Itagi Huilgol et al [2], [3], [4].…”

“…The concept of distance degree injective graphs was introduced by Bloom et al in [25]. A graph G is said to be a distance degree injective (DDI) graph if no two of its vertices have the same distance degree sequence.…”

Regular graphs having the same path layer matrix

“…2, [141][142][143][144][145][146][147][148] (1990) 0 1990 by John Wiley & Sons, Inc. It is obvious that the path layer matrix T ( G ) coincides with the path degree sequence of a graph G [2,8] and the Atomic Path Code of a molecule [9]. The path layer matrix and its modifications were used as topological indices (graph invariants) for characterization of a structure of molecular graphs [9][10][11].…”

Cubic graphs without cut‐vertices having the same path layer matrix

“…This invariant and its modi®cations have found interesting applications in chemistry for the characterization of branching in molecules, for establishing similarity of molecular graphs, and for drug design [10±13]. For trees a path layer matrix coincides with a layer matrix (or distance degree sequence [1]), since any two vertices in a tree are connected by a unique path. Investigations of these matrices deal with ®nding a pair of nonisomorphic graphs having some speci®ed property such that both graphs have the same matrix [1±4,6±9, 14,15].…”