D-Spectrum and D-Energy of Complements of Iterated Line Graphs of Regular Graphs

commuting and non -commuting graphs of finit groups

فرض کنیمg یک گروه غیر آبلی متناهی باشد . گراف جابجایی g که با نماد نمایش داده می شود ،گرافی است ساده با مجموعه رئوس که در آن دو راس با یک یال به هم وصل می شوند اگر و تنها اگر . مکمل گراف جابجایی g راگراف نا جابجایی g می نامیم.و با نماد نشان می دهیم. گرافهای جابجایی و ناجابجایی یک گروه متناهی ،اولین بار توسطاردوش1 مطرح گردید ،ولی در سالهای اخیر به طور مفصل در مورد بحث و بررسی قرار گرفتند . در ،م...

The spectrum of the hyper-star graphs and their line graphs

Let n 1 be an integer. The hypercube Qn is the graph whose vertex set isf0;1gn, where two n-tuples are adjacent if they differ in precisely one coordinate. This graph has many applications in Computer sciences and other area of sciences. Inthe graph Qn, the layer Lk is the set of vertices with exactly k 1’s, namely, vertices ofweight k, 1 k n. The hyper-star graph B(n;k) is...

D-bounded Distance-regular Graphs

Let Γ = (X, R) denote a distance-regular graph with diameter D ≥ 3 and distance function δ. A (vertex) subgraph ∆ ⊆ X is said to be weak-geodetically closed whenever for all x, y ∈ ∆ and all z ∈ X, δ(x, z) + δ(z, y) ≤ δ(x, y) + 1 −→ z ∈ ∆. Γ is said to be D-bounded whenever for all x, y ∈ X, x, y are contained in a common regular weak-geodetically closed subgraph of diameter δ(x, y). Assume Γ i...

d-Regular Graphs of Acyclic Chromatic Index

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a′(G). It was conjectured by Alon, Sudakov and Zaks (and earlier by Fiamcik) that a′(G)≤ +2, where = (G) denotes the maximum degree of the graph. Alon e...

The asymptotic behavior of some indices of iterated line graphs of regular graphs

Regular Star Complements in Strongly Regular Graphs

We prove that, aside from the complete multipartite graphs and graphs of Steiner type, there are only finitely many connected strongly regular graphs with a regular star complement of prescribed degree s ∈ IN . We investigate the possible parameters when s ≤ 5. AMS Classification: 05C50