Decomposing split graphs into locally irregular graphs
نویسندگان
چکیده
A graph is locally irregular if any pair of adjacent vertices have distinct degrees. decomposition a G D such that every subgraph H∈D irregular. said to be decomposable it admits decomposition. We prove split can decomposed into at most three subgraphs and we characterize all graphs whose one, two or subgraphs.
منابع مشابه
Decomposing oriented graphs into 6 locally irregular oriented graphs
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...
متن کاملDecomposing Oriented Graphs into Six Locally Irregular Oriented Graphs
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...
متن کاملOn Decomposing Graphs of Large Minimum Degree into Locally Irregular Subgraphs
A locally irregular graph is a graph whose adjacent vertices have distinct degrees. We say that a graph G can be decomposed into k locally irregular subgraphs if its edge set may be partitioned into k subsets each of which induces a locally irregular subgraph in G. It has been conjectured that apart from the family of exceptions which admit no such decompositions, i.e., odd paths, odd cycles an...
متن کاملEdge-partitioning graphs into regular and locally irregular components
A graph is locally irregular if every two adjacent vertices have distinct degrees. Recently, Baudon et al. introduced the notion of decomposition into locally irregular subgraphs. They conjectured that for almost every graphG, there exists a minimum integer χirr(G) such thatG admits an edge-partition into χ ′ irr(G) classes, each of which induces a locally irregular graph. In particular, they c...
متن کاملNeighbourly Irregular Derived Graphs
A connected graph G is said to be neighbourly irregular graph if no two adjacent vertices of G have same degree. In this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2021
ISSN: ['1872-6771', '0166-218X']
DOI: https://doi.org/10.1016/j.dam.2020.12.002