Ascending Bi-Pendant Domination Decomposition of Path and Cycle

Path and cycle decomposition numbers

Path Partitions, Cycle Covers and Integer Decomposition

A polyhedron P has the integer decomposition property, if every integer vector in kP is the sum of k integer vectors in P . We explain that the projections of polyhedra defined by totally unimodular constraint matrices have the integer decomposition property, in order to deduce the same property for coflow polyhedra defined by Cameron and Edmonds. We then apply this result to the convex hull of...

Domination Integrity of Line Splitting Graph and Central Graph of Path, Cycle and Star Graphs

The domination integrity of a connected graph G = (V (G), E(G)) is denoted as DI(G) and defined by DI(G) = min{|S| + m(G − S)}, where S is a dominating set and m(G − S) is the order of a maximum component of G− S. This paper discusses domination integrity of line splitting graph and central graph of some graphs.

BI - DIRECTIONAL PATH TRACINGEric

In this paper we present a new Monte Carlo rendering algorithm that seamlessly integrates the ideas of shooting and gathering power to create photorealistic images. The algorithm can be explained as a generalisation of the well-known path tracing algorithm. Test results show that it performs signiicantly better for typical indoor scenes where indirect lighting is important.

Bi-Gyrogroup: The Group-Like Structure Induced by Bi-Decomposition of Groups

‎The decomposition $Gamma=BH$ of a group $Gamma$ into a subset B ‎and a subgroup $H$ of $Gamma$ induces‎, ‎under general conditions‎, ‎a ‎group-like structure for B‎, ‎known as a gyrogroup‎. ‎The famous‎ concrete realization of a gyrogroup‎, ‎which motivated the emergence ‎of gyrogroups into the mainstream‎, ‎is the space of all ‎relativistically admissible velocities along with a binary ‎mbox{...