Two classes of graphs which are maximal with respect to the absence of Hamiltonian paths are presented. Block graphs with this property are characterized.

Edge shift distance between isomorphism classes of graphs, introduced by M. Johnson, is investigated in the case of trees and compared with other distances .

The paper studies the domatic numbers and the total domatic numbers of graphs having cut-vertices. We shall study the domatic number d(G) and the total domatic number d t (G) of a graph G. A surveyâ€¦ (More)

A graph G is called locally s-regular if the neighbourhood of each vertex of G induces a subgraph of G which is regular of degree s. We study graphs which are locally s-regular and simultaneouslyâ€¦ (More)

We study three recently introduced numerical invariants of graphs, namely, the signed domination number y., the minus domination number 7 and the majority domination number ymaj. An upper bound forâ€¦ (More)

This lecture treats some problems from the book in [2] by E. Prisner. All these problems concern graph operators. A graph operator is a mapping to which every graph G from some class of graphsâ€¦ (More)