arXiv subjects

Abdelkader Khelladi

Publications and source records attributed to Abdelkader Khelladi.

3 recordsLinked to original sources

arXiv2019

Transitive closure and transitive reduction in bidirected graphs

In a bidirected graph an edge has a direction at each end, so bidirected graphs generalize directed graphs. We generalize the definitions of transitive closure and transitive reduction from directed graphs to bidirected graphs by introducing new notions of bipath and bicircuit that generalize directed paths and cycles. We show how transitive reduction is related to transitive closure and to the matroids of the signed graph corresponding to the bidirected graph.

math.CO↗

arXiv2017

New concept of connection in signed graphs

In a signed graph each edge has a sign, $+1$ or $-1$. We introduce in the present paper a new definition of connection in a signed graph by the existence of both positive and negative chains between vertices. We prove some results and properties of this definition, such as sign components, sign articulation vertices, and sign isthmi, and we compare them to corresponding graph and signed-graphic matroid properties. We apply our results to signed graphs without positive cycles. For signed graphs in which every edge is negative our properties become parity properties.

math.CO↗

arXiv2007

Connection between ordinary multinomials, generalized Fibonacci numbers, partial Bell partition polynomials and convolution powers of discrete uniform distribution

Using an explicit computable expression of ordinary multinomials, we establish three remarkable connections, with the q-generalized Fibonacci sequence, the exponential partial Bell partition polynomials and the density of convolution powers of the discrete uniform distribution. Identities and various combinatorial relations are derived.

math.CO↗