45 research outputs found
Small cycles, generalized prisms and Hamiltonian cycles in the Bubble-sort graph
The Bubble-sort graph , is a Cayley graph over the
symmetric group generated by transpositions from the set . It is a bipartite graph containing all even cycles of
length , where . We give an explicit
combinatorial characterization of all its - and -cycles. Based on this
characterization, we define generalized prisms in , and
present a new approach to construct a Hamiltonian cycle based on these
generalized prisms.Comment: 13 pages, 7 figure
The Wiener Polynomial Derivatives and Other Topological Indices in Chemical Research
Wiener polynomial derivatives and some other information and topological indices are investigated with respect to their discriminating power and property correlating ability
An improved bound on the chromatic number of the Pancake graphs
In this paper an improved bound on the chromatic number of the Pancake graph
, is presented. The bound is obtained using a subadditivity
property of the chromatic number of the Pancake graph. We also investigate an
equitable coloring of . An equitable -coloring based on efficient
dominating sets is given and optimal equitable -colorings are considered for
small . It is conjectured that the chromatic number of coincides with
its equitable chromatic number for any
A general construction of strictly Neumaier graphs and related switching
In this paper we propose a construction of Neumaier graphs with nexus 1,
which generalises two known constructions. We then discuss small strictly
Neumaier graphs obtained from the general construction and give a geometric
description for some of them. Finally, we apply a variation of the Godsil-McKay
switching to the general construction
Spectra of strongly Deza graphs
A Deza graph with parameters is a -regular graph with
vertices such that any two distinct vertices have or common neighbours.
The children and of a Deza graph are defined on the vertex set
of such that every two distinct vertices are adjacent in or if
and only if they have or common neighbours, respectively. A strongly
Deza graph is a Deza graph with strongly regular children. In this paper we
give a spectral characterisation of strongly Deza graphs, show relationships
between eigenvalues, and study strongly Deza graphs which are distance-regular