Martin Bača

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 of graphs the precise values of these parameters are proved.

On topological indices of fullerenes

Two degree based topological indices, the atom-bond connectivity (ABC) and the geometric-arithmetic (GA) indices of fullerene networks and carbon nanotube networks are studied. Expressions for ABC and GA indices for these important classes of networks are obtained.

The metric dimension of the lexicographic product of graphs

Abstract A set of vertices W resolves a graph G if every vertex is uniquely determined by its coordinate of distances to the vertices in W . The minimum cardinality of a resolving set of G is called the metric dimension of G . In this paper, we consider a graph which is obtained by the lexicographic product between two graphs. The lexicographic product of graphs G and H , which is denoted by G ∘ H , is the graph with vertex set V ( G ) × V ( H ) = { ( a , v ) | a ∈ V ( G ) , v ∈ V ( H ) } , where ( a , v ) is adjacent to ( b , w ) whenever a b ∈ E ( G ) , or a = b and v w ∈ E ( H ) . We give the general bounds of the metric dimension of a lexicographic product of any connected graph G and an arbitrary graph H . We also show that the bounds are sharp.

Edge-antimagic graphs

For a graph G=(V,E), a bijection g from V(G)@?E(G) into {1,2,...,|V(G)|+|E(G)|} is called (a,d)-edge-antimagic total labeling of G if the edge-weights w(xy)=g(x)+g(y)+g(xy), xy@?E(G), form an arithmetic progression starting from a and having common difference d. An (a,d)-edge-antimagic total labeling is called super (a,d)-edge-antimagic total if g(V(G))={1,2,...,|V(G)|}. We study super (a,d)-edge-antimagic properties of certain classes of graphs, including friendship graphs, wheels, fans, complete graphs and complete bipartite graphs.

( a,d )-edge-antimagic total labelings of caterpillars

For a graph G = (V,E), a bijection g from V(G) ∪ E(G) into { 1,2, ..., ∣ V(G) ∣ + ∣ E(G) ∣ } is called (a,d)-edge-antimagic total labeling of G if the edge-weights w(xy) = g(x) + g(y) + g(xy), xy ∈ E(G), form an arithmetic progression with initial term a and common difference d. An (a,d)-edge-antimagic total labeling g is called super (a,d)-edge-antimagic total if g(V(G)) = { 1,2,..., ∣ V(G) ∣ } . We study super (a,d)-edge-antimagic total properties of stars Sn and caterpillar Sn1,n2,...,nr.

Vertex-antimagic total labelings of graphs

In this paper we introduce a new type of graph labeling, the

On magic labelings of honeycomb

(a, d)

Total edge irregularity strength of generalized prism

- vertex-antimagic total labeling, which is a generalization of several other types of labelings. A connected graph

On magic labelings of type (1,1,1) for the special class of plane graphs

G(V,E)

On super (a,1)-edge-antimagic total labelings of regular graphs

is said to be