The cycle and co-cycle matroids of a bond graph are defined using chain group matroids derived,from the cycle and co-cycle vector spaces qf a bond graph. The relationship between these structures is investigated and various results are proved. A precise equivalence is dejined for bond graphs. Duality theory is seen to be very clear in the context of bond graph matroids.

An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, ΣνεV(H) f(v) +  ΣeεE(H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥ ...

An H-magic labeling in a H-decomposable graph G is a bijection f : V (G) ∪ E(G) → {1, 2, ..., p + q} such that for every copy H in the decomposition, ∑νεV (H) f(v) + ∑νεE (H) f(e) is constant. f is said to be H-E-super magic if f(E(G)) = {1, 2, · · · , q}. A family of subgraphs H1,H2, · · · ,Hh of G is a mixed cycle-decomposition of G if every subgraph Hi is isomorphic to some cycle Ck, for k ≥...

This paper was designed to provide an introduction to the vector spaces used in graph theory. In graph theory, an area of mathematics, a cycle space is a vector space defined from an undirected graph; elements of the cycle space represent formal combinations of cycles in the graph. Cycle spaces allow one to use the tools of linear algebra to study graphs. A cycle basis is a set of cycles that g...

We consider the problem of computing a minimum cycle basis in a directed graph. The input to this problem is a directed graph G whose edges have nonnegative weights. A cycle in this graph is actually a cycle in the underlying undirected graph with edges traversable in both directions. A {−1, 0, 1} edge incidence vector is associated with each cycle: edges traversed by the cycle in the right dir...

Definition 1 A Hamiltonian cycle in a graph is a cycle that visits each vertex exactly once. A Hamiltonian graph is a graph that contains a Hamiltonian cycle. It is well known that the problem of determining if a graph is Hamiltonian is N P-complete. Here we will construct a NIZK proof in the hidden-bits model (HBM) that is able to prove that a graph is Hamiltonian. First we define how graphs a...