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On irregular total labellings
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 ofExpand
The train marshalling problem
TLDR
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
Characterization of eccentric digraphs
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 atExpand
Cayley graphs as classifiers for data mining: The influence of asymmetries
TLDR
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
Antimagic Labelings of Generalized Petersen Graphs That Are Plane
A Note on Constructing Large Cayley Graphs of Given Degree and Diameter by Voltage Assignments
TLDR
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
The sum number of the cocktail party graph
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 aExpand
On distance magic labeling of graphs
Antimagic labeling of generalized pyramid graphs
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 vertexExpand
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