We show that every 4-representative graph embedding in the double torus contains a noncontractible cycle which separates the surface into two pieces. This improves a result of Zha and Zhao for general orientable surfaces, in which the same conclusion holds for 6-representative graph embeddings. Noncontractible separating cycles have been studied because they provide a way to do induction on the...

We define a construction operation on hypergraphs using a colimit and show that its expressiveness concerning graph rewriting is equal to the graph expressions of Courcelle and the double-pushout approach of Ehrig. With an inductive way of representing graphs, graph rewriting arises naturally as a derived concept. The usefulness of our approach for the compositional modelling of concurrent syst...

We develop a new method for building a representation of an image from a library of basis elements that is facilitated by a joint adaptive space and frequency (JASF) graph. The JASF graph combines partitionable frequency expansion and spatial segmentation of the image, symmetrically. We demonstrate by using a rate-distortion framework for basis selection that the JASF graph improves compression...

A graph is supereulerian if it has a spanning eulerian subgraph. There is a reduction method to determine whether a graph is supereulerian, and it can also be applied to study other concepts, e.g., hamiltonian line graphs, a certain type of double cycle cover, and the total interval number of a graph. We outline the research on supereulerian graphs, the reduction method and its applications.

In this paper, we introduce weighted graph bundles and study their characteristic polynomial. In particular, we show that the characteristic polynomial of a weighted K2 (K2)bundles over a weighted graph F can be expressed as a product of characteristic polynomials two weighted graphs whose underlying graphs are F As an application, we compute the signature of a link whose corresponding weighted...

An orthogonal double cover (ODC) of a complete graph is a collection of graphs such that every two of them share exactly one edge and every edge of the complete graph belongs to exactly two of the graphs. In this paper, we construct ODCs of Kn where all graphs are isomorphic to certain spanning subgraphs G (such as co-triangles, a star with cotriangles, and two other graph classes).

We explore the networks that yield the largest mean consensus time of voter models under different update rules. By analytical and numerical means, we show that the so-called lollipop graph, barbell graph, and double star graph maximise the mean consensus time under the update rules called the link dynamics, voter model, and invasion process, respectively. For each update rule, the largest mean...

We explore the networks that yield the largest mean consensus time of voter models under different update rules. By analytical and numerical means, we show that the so-called lollipop graph, barbell graph, and double-star graph maximize the mean consensus time under the update rules called the link dynamics, voter model, and invasion process, respectively. For each update rule, the largest mean...

‎let $d_{n,m}=big[frac{2n+1-sqrt{17+8(m-n)}}{2}big]$ and‎ ‎$e_{n,m}$ be the graph obtained from a path‎ ‎$p_{d_{n,m}+1}=v_0v_1 cdots v_{d_{n,m}}$ by joining each vertex of‎ ‎$k_{n-d_{n,m}-1}$ to $v_{d_{n,m}}$ and $v_{d_{n,m}-1}$‎, ‎and by‎ ‎joining $m-n+1-{n-d_{n,m}choose 2}$ vertices of $k_{n-d_{n,m}-1}$‎ ‎to $v_{d_{n,m}-2}$‎. ‎zhang‎, ‎liu and zhou [on the maximal eccentric‎ ‎connectivity ind...