Two new graph characteristics, the total vertex irregularity strength and the total edge irregularity strength, are introduced. Estimations on these parameters are obtained. For some families of… Expand

The aim of this paper is to show that the decision problem: “Given numbers n,k and a partition S of {1,2,…,n}, is K(S)⩽k?” is NP-complete and to give a general upper bound for K( S) in terms of n.Expand

The eccentric digraphED(G) of a digraph G represents the binary relation, defined on the vertex set of G, of being 'eccentric'; that is, there is an arc from u to v in ED(G) if and only if v is at… Expand

This paper proposes a new method of using Cayley graphs for classification of data using the endomorphism monoids of graphs, a convenient tools expressing asymmetries of the graphs.Expand

It is shown that all of the currently known largest graphs of degree $\le 15$ and diameter $\le 10$ have been found by computer search among Cayley graphs of semidirect products of cyclic groups, and all of them can in fact be described as lifts of smaller Cayley graph of cycling groups, with voltages in (other) cyclicgroups.Expand

A graph G is called a sum graph if there exists a labelling of the vertices of G by distinct positive integers such that the vertices labelled u and v are adjacent if and only if there exists a… Expand

An antimagic labeling of a graph with q edges is a bijection from the set of edges to the set of positive integers {1, 2, ..., q} such that all vertex weights are pairwise distinct, where the vertex… Expand