In graph theory, a branch of mathematics, the (binary) cycle space of an undirected graph is the set of its even-degree subgraphs. This set of subgraphs can be described algebraically as a vector space over the two-element finite field. The dimension of this space is …

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space is the given vector subspace. For a digraph D, we are interested in the integral basis matrix B of the tension space T(D) and the basis matrix C of the °ow space F(D). For an edge subset S µ A(D), we denote by BjS (or just BS) the submatrix of B consisting of the columns of B that are labeled by members of S. Given a maximal spanning ...

2015年6月22日 · Definition (Cycle space): Let $G=(V,E)$ . The cycle space of $G$ is an element of $2^{E}$ denoted $\mathcal{C}$ and is the smallest set (of sets) containing the $\emptyset$, all cycles in $G$ and (where each cycle is treated as a set …

We present a new ‘singular’ approach that builds the cycle space of a graph not on its finite cycles but on its topological circles, the homeomorphic images of S1 in the space formed by the graph together with its ends.

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The book is a fundamental reference book on cycle space theory, and important for current research in complex geometry; The book is an essential complement to the first volume for doctoral students in complex geometry; The book shows how local complex geometry may enlighten projective geometry

studied combinatorial aspects of graphs. Particularly, we look at graph coverings, gain graphs, and the cycle space of a graph. One of the main contributions of this paper is to develop connections between each of these disparate areas of graph theory. In particular, we provide a combinatorial interpretation of the rst path homology group.

2017年10月3日 · We study graph coverings, gain graphs, and cycle spaces of graphs, in addition to the Bakry-Émery curvature and the path homology. The main results follow as a consequence of several different relationships developed among these different areas.