An undirected graph G is locally irregular if every two of its adjacent vertices have distinct degrees. We say that G is decomposable into k locally irregular graphs if there exists a partition E1∪E2∪ ...∪Ek of the edge set E(G) such that each Ei induces a locally irregular graph. It was recently conjectured by Baudon et al. that every undirected graph admits a decomposition into 3 locally irre...

The wildfire prediction model is crucial for accurate rescue and rapid evacuation. Existing models mainly adopt regular grids or fire perimeters to describe the landscape. However, these have difficulty in explicitly demonstrating local spread details, especially a complex In this paper, we propose with an irregular graph network (IGN). This implemented IGN generation algorithm characterize wil...

An undirected graph G is locally irregular if every two of its adjacent vertices have distinct degrees. We say that G is decomposable into k locally irregular graphs if there exists a partition E1∪E2∪ ...∪Ek of the edge set E(G) such that each Ei induces a locally irregular graph. It was recently conjectured by Baudon et al. that every undirected graph admits a decomposition into 3 locally irre...

A vertex irregular total k-labeling of a graph G with vertex set V and edge set E is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of G, denoted by tvs(G)is the minimum value of the largest label k over all such irregular assignment. In this paper, we study the to...

A simple connected graph is highly irregular if each of its vertices is adjacent only to vertices with distinct degrees. In this paper we find: (1) the greatest number of edges of a highly irregular graph with n vertices, where n is an odd integer (for n even this number is given in [1]), (2) the smallest number of edges of a highly irregular graph of given order.

Vague graphs (VGs), belonging to the fuzzy (FGs) family, have good capabilities when faced with problems that cannot be expressed by FGs. The notion of a VG is new mathematical attitude model ambiguity and uncertainty in decision-making issues. A vague graph structure (VFGS) generalization VG. It powerful useful tool find influential person various relations. VFGSs can deal associated inconsist...