compiled April 30, 2009 from draft version hg:e0660c153c0b:79 An acyclic coloring of a graph is a proper vertex coloring such that the subgraph induced by the union of any two color classes is a disjoint collection of trees. The more restricted notion of star coloring requires that the union of any two color classes induces a disjoint collection of stars. The acyclic and star chromatic numbers ...

It is shown that the Trivalent Cayley graphs, TC,,, are near recursive. In particular, TC, is a union of four copies of i”Cn_2 with additional well placed nodes. This allows one to recursively build the Hamilton cycle in TC,.

In this paper, some properties of union and join on total regular intuitionistic fuzzy graphs are derived, and also theorems related to these concepts are stated and proved. AMS Mathematics Subject Classification (2010): 03E72, 05C72.

For a knotted graph in S* we define the vertex constant group, a quotient of the fundamental group of the complement. For planar graphs the group is cyclic. For graphs with periodic symmetry the group is related to the fundamental group of the branched cover of S3 branched over knots contained in the quotient of the graph under the symmetry. These tools are used to demonstrate that a large fami...

The existence of a connected 12-regular {K4,K2,2,2}-ultrahomogeneous graph G is established, (i.e. each isomorphism between two copies of K4 or K2,2,2 in G extends to an automorphism of G), with the 42 ordered lines of the Fano plane as vertices and an adjacency resembling that of star Cayley graphs. The graph G can be expressed in a unique way both as the edge-disjoint union of 42 induced copi...

reliability wiener number is a modification of the original wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain condition...

For a knotted graph in S3 we define the vertex constant group, a quotient of the fundamental group of the complement. For planar graphs the group is cyclic. For graphs with periodic symmetry the group is related to the fundamental group of the branched cover of S3 branched over knots contained in the quotient of the graph under the symmetry. These tools are used to demonstrate that a large fami...

Let G be a (finite) group and let S be a non-empty subset of G. The vertex set of the orbit graph O(G,S) is the union, over all s ∈ S, of orbits of left translations induced by s. If u and v are distinct vertices (each representing an orbit of some s and t from S), then for any g ∈ G appearing in both orbits there is an edge coloured g in O(G,S) joining u and v. Orbit graphs are an important sp...

  Abstract   Background: The tibial diaphyseal fractures are the most common type of long   bone fractures encountered by most orthopedic surgeons. In accordance with descriptive indices of tibia fractures on the basis of their location in the bone, distal tibia   fractures have the second incidence of all tibia fractures after the middle tibia fractures.   The purpose of the study was to asses...