Yap introduced in [12] (J. Graph Theory (5 (1981) 159) a method for constructing -critical graphs. The construction has been extended by Plantholt [8] (J. Graph Theory 9 (1985) 371), Hilton and Zhao [5] (Discrete Appl. Math. 76 (1997) 205), and McMichael [6] (Preprint). It was shown in [5] that if G∗ is a graph obtained by splitting any vertex into two vertices from a -regular class 1 graph G, ...

Let A = M N E IR nn be a splitting. We investigate the spectral properties of the iteration matrix M 1 N by considering the relationships of the graphs of A, M, N, and M1 N. We call a splitting an M-splitting if M is a nonsingular M-matrix and N;;. O. For an M-splitting of an irreducible Z-matrix A we prove that the circuit index of M1 N is the greatest common divisor of certain sets of integer...

define minimal \;01un:lal:ne'IlLS, In contrast with [8),

In this paper, we use the concept of graph convergence of H(.,.)-co-accretive mapping introduced by [R. Ahmad, M. Akram, M. Dilshad, Graph convergence for the H(.,.)-co-accretive mapping with an application, Bull. Malays. Math. Sci. Soc., doi: 10.1007/s40840-014-0103-z, 2014$] and define an over-relaxed proximal point method to obtain the solution of a generalized variational inclusion problem ...

We present a novel algorithm for efficiently splitting deformable solids along arbitrary piecewise linear crack surfaces in cutting and fracture simulations. The algorithm combines a meshless discretization of the deformation field with explicit surface tracking using a triangle mesh. We decompose the splitting operation into a first step where we synthesize crack surfaces, and a second step wh...

The Birkhoff-von Neumann (BVN) strategy for offline switching does not support multicast, as it considers only permutation-based switch configurations. This thesis extends the BVN strategy to multicast switching. Using a graph theoretic model, we show that the capacity region for a traffic pattern is precisely the stable set polytope of the pattern's "conflict graph", in the no-fanout-splitting...