A locally irregular graph is a in which the end vertices of every edge have distinct degrees. coloring G any such that each colors induces subgraph G. colorable if it allows coloring. The chromatic index G, denoted by χirr′(G), smallest number used local irregularity conjecture claims all graphs, except odd-length paths, cycles and certain class cacti are three colors. As valid for graphs with ...

In a graph G, vertex (resp. an edge) metric generator is set of vertices S such that any pair edges) from G distinguished by at least one S. The cardinality smallest the dimension G. Sedlar and Škrekovski (0000) we determined unicyclic graphs it takes its value two consecutive integers. Therein, several cycle configurations were introduced greater values only if these present in graph. this pap...

The Randić index of an organic molecule whose molecular graph is G is the sum of the weights (d(u)d(v))− 1 2 of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G. In the paper, we give a sharp lower bound on the Randić index of cacti.

In this paper we determine, or give lower and upper bounds on, the 2-dipath and oriented L(2, 1)-span of the family of planar graphs, planar graphs with girth 5, 11, 16, partial k-trees, outerplanar graphs and cacti.

Despite the fact that parrots (Psitacifformes) are generalist apex frugivores, they have largely been considered plant antagonists and thus neglected as seed dispersers of their food plants. Internal dispersal was investigated by searching for seeds in faeces opportunistically collected at communal roosts, foraging sites and nests of eleven parrot species in different habitats and biomes in the...

Without further ado, we present the P3-game. The P3-game is decidable for elementary classes of graphs such as paths and cycles. From an algorithmic point of view, the connected P3-game is fascinating. We show that the connected P3-game is polynomially decidable for classes such as trees, chordal graphs, ladders, cacti, outerplanar graphs and circular arc graphs.

These are notes of a mini-course given at Dennisfest in June 2001. The goal of these notes is to give a self-contained survey of deformation quantization, operad theory, and graph homology. Some new results related to “String Topology” and cacti are announced in Section 2.7.

In this paper we study the L(2, 1)-labeling problem on oriented planar graphs with particular attention on the subclasses of oriented prisms, Halin and cactus graphs. For these subclasses more accurate results are presented. keywords: L(2, 1)-labeling, oriented graph coloring, digraphs, prisms, Halin graphs, cacti.