Center and periphery of lexicographic product of digraphs
نویسندگان
چکیده
Let D = (V,E) be a digraph and u, v ∈ V. The metric maximum distance is defined by md(u,v) max {d⃗(u,v), d⃗(v,u)}, where d⃗(u,v) denote the length of shortest directed u − path in D. m-eccentricity vertex mecc(v) {md(v,u) : V(D)}. m-center mC(D) strongly connected consists all vertices with minimum m-eccentricity, m-periphery mPer(D) relationship between two digraphs their lexicographic product studied this article.
منابع مشابه
Cayley digraphs and lexicographic product ∗
In this paper, we prove that a Cayley digraph Γ = Cay(G, S) is a nontrivial lexicographical product if and only if there is a nontrivial subgroup H of G such that S \ H is a union of some double cosets of H in G.
متن کاملThe Center and Periphery of Composite Graphs
The center (periphery) of a graph is the set of vertices with minimum (maximum) eccentricity. In this paper, the structure of centers and peripheries of some classes of composite graphs are determined. The relations between eccentricity, radius and diameter of such composite graphs are also investigated. As an application we determine the center and periphery of some chemical graphs such as nan...
متن کاملthe center and periphery of composite graphs
the center (periphery) of a graph is the set of vertices with minimum (maximum)eccentricity. in this paper, the structure of centers and peripheries of some classes ofcomposite graphs are determined. the relations between eccentricity, radius and diameterof such composite graphs are also investigated. as an application we determinethe center and periphery of some chemical graphs such as nanotor...
متن کاملManhattan Product of Digraphs
We review the Manhattan product of digraphs from the viewpoint of spectral analysis and obtain some preliminary formulae. As an example, the spectrum of the Manhattan product of the directed path Pn and the directed cycle C2 is obtained as well as its asymptotic spectral distribution.
متن کاملLexicographic Product of Extendable Graphs
Lexicographic product G◦H of two graphs G and H has vertex set V (G)×V (H) and two vertices (u1, v1) and (u2, v2) are adjacent whenever u1u2 ∈ E(G), or u1 = u2 and v1v2 ∈ E(H). If every matching of G of size k can be extended to a perfect matching in G, then G is called k-extendable. In this paper, we study matching extendability in lexicographic product of graphs. The main result is that the l...
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: The art of discrete and applied mathematics
سال: 2023
ISSN: ['2590-9770']
DOI: https://doi.org/10.26493/2590-9770.1639.4c9