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Abstract: In their study of fundamental groups of one-dimensional path-connected compact metric spaces, Cannon and Conner have asked: Is there a tree-like object that might be considered the topologic...
Abstract: We construct a state model for the two-variable Kauffman polynomial using planar trivalent graphs. We also use this model to obtain a polynomial invariant for trivalent graphs embedded in th...
Abstract: A geometric graph G(bar) is a simple graph drawn in the plane, on points in general position, with straight-line edges. We call G(bar) a geometric realization of the underlying abstract grap...
Abstract: We construct travelling wave graphs of the form $z=-ct+\phi(x)$, $\phi: x \in \mathbb{R}^{N-1} \mapsto \phi(x)\in \mathbb{R}$, $N \geq 2$, solutions to the $N$-dimensional forced mean curvat...
Abstract: We treat the stationary (cubic) nonlinear Schr\"odinger equation (NSLE) on simplest graphs. Formulation of the problem and exact analytical solutions of NLSE are presented for star graphs co...
Abstract: We construct two families of distance-regular graphs, namely the subgraph of the dual polar graph of type B_3(q) induced on the vertices far from a fixed point, and the subgraph of the dual ...
Abstract: In this paper we introduce the nullity of signed graphs, and give some results on the nullity of signed graphs with pendant trees. We characterize the unicyclic signed graphs of order n with...
Abstract: A sender wishes to broadcast an n character word x in F^n (for a field F) to n receivers R_1,...,R_n. Every receiver has some side information on x consisting of a subset of the characters o...
Abstract: A number of computations exist, especially in area of error-control coding and matrix computations, whose underlying data flow graphs are based on finite projective-geometry(PG) based balanc...
Abstract: In this paper, we develop a diamond graph theory and apply the theory to the (co)homology of the Lie algebra generated by positive systems of the classical semi-simple Lie algebras over the ...
Abstract: An identifying code of a graph is a subset of its vertices such that every vertex of the graph is uniquely identified by the set of its neighbours within the code. We study the edge-identify...
Abstract: Non-equilibrium steady states of quantum fields on star graphs are explicitly constructed. These states are parametrized by the temperature and the chemical potential, associated with each e...
Abstract: Given a finitely generated amenable group we consider ergodic random Schr\"odinger operators on a Cayley graph with random potentials and random boundary conditions. We show that the normali...
Motif based hierarchical random graphs: structural properties and critical points of an Ising model.

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