
We describe an algorithm that uses
A vertex set
for each graph
if
if
A caterpillar
In the theory of cocyclic self-dual codes, three types of equivalences are encountered: cohomology or the equivalence of cocycles, Hadamard equivalence or the equivalence of Hadamard matrices, and the equivalence of binary linear codes. There are some results relating the latter two equivalences, see Ozeki [12], but not when the Hadamard matrices are un-normalised.
Recently, Horadam [9] discovered shift action, whereby every finite group
Here we show that shift-equivalent cocycles generate equivalent Hadamard matrices and that shift-equivalent cocyclic Hadamard matrices generate equivalent binary linear codes.
New identities involving the Catalan sequence ordinary generating function are developed, and a previously known one established from first principles using a hypergeometric approach.
We examine words
For constructing routes in mobile ad-hoc networks (MANET) and sensor networks, it is highly desirable to perform primitive computations locally. If a network can be represented in the doubly connected edge list (DCEL) data structure, then many operations can be done locally. However, the DCEL data structure can be used to represent only planar graphs. In this paper, we propose an extended version of the DCEL data structure called ExtDCEL that can be used for representing non-planar graphs as well as their planar components. The proposed data structure can be used to represent geometric networks in mobile computing that include unit disk graphs, Gabriel graphs, and constrained Delaunay triangulations. We show how the proposed data structure can be used to implement a hybrid greedy face routing algorithm in optimum
In this paper, we study the decomposition of the graph
In this paper, we consider the problem of the non-existence of some orthogonal arrays (O-arrays) of strength four with two levels, the number of constraints
We give a constructive proof that a planar graph on
This paper answers the question as to whether every natural number
A
We use a new technique for decomposition of complete graphs with even number of vertices based on
A constant composition code of length
In this paper, we develop a computational method for constructing transverse
A vertex-magic total labeling of a graph
In this paper, we present a technique for constructing vertex-magic total labelings of products of certain vertex-magic total
At each vertex in a Cayley map, the darts emanating from that vertex are labeled by a generating set of a group. This generating set is closed under inverses. Two classes of Cayley maps are balanced and antibalanced maps. For these cases, the distributions of the inverses about the vertex are well understood. For a balanced Cayley map, either all the generators are involutions or each generator is directly opposite across the vertex from its inverse. For an antibalanced Cayley map, there is a line of reflection in the tangent plane of the vertex so that the inverse generator for each dart label is symmetric across that line. An
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