Distance spectrum and energy of graphs with small diameter
نویسندگان
چکیده
منابع مشابه
Tight Distance-regular Graphs with Small Diameter
We prove the following bound for a k regular graph on n vertices with nontrivial eigenvalues from the interval r s n k rs k r k s Equality holds if and only if the graph is strongly regular with eigenvalues in fk s rg Nonbipartite distance regular graphs with diameter d and eigenvalues k d whose local graphs satisfy the above bound with equality for s b and r b d are called tight graphs and are...
متن کاملD-Spectrum and D-Energy of Complements of Iterated Line Graphs of Regular Graphs
The D-eigenvalues {µ1,…,µp} of a graph G are the eigenvalues of its distance matrix D and form its D-spectrum. The D-energy, ED(G) of G is given by ED (G) =∑i=1p |µi|. Two non cospectral graphs with respect to D are said to be D-equi energetic if they have the same D-energy. In this paper we show that if G is an r-regular graph on p vertices with 2r ≤ p - 1, then the complements of iterated lin...
متن کاملSuperconnectivity of regular graphs with small diameter
A graph is superconnected, for short super-κ, if all minimum vertex-cuts consist of the vertices adjacent with one vertex. In this paper we prove for any r-regular graph of diameter D and odd girth g that if D ≤ g − 2, then the graph is super-κ when g ≥ 5 and a complete graph otherwise.
متن کاملConnectivity and diameter in distance graphs
For n ∈ N and D ⊆ N, the distance graph P n has vertex set {0, 1, . . . , n− 1} and edge set {ij | 0 ≤ i, j ≤ n − 1, |j − i| ∈ D}. The class of distance graphs generalizes the important and very well-studied class of circulant graphs which have been proposed for numerous network applications. In view of fault tolerance and delay issues in these applications, the connectivity and diameter of cir...
متن کاملEigenvalues, diameter, and mean distance in graphs
It is well-known that the second smallest eigenvalue 22 of the difference Laplacian matrix of a graph G is related to the expansion properties of G. A more detailed analysis of this relation is given. Upper and lower bounds on the diameter and the mean distance in G in terms of 22 are derived.
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: Applicable Analysis and Discrete Mathematics
سال: 2017
ISSN: 1452-8630,2406-100X
DOI: 10.2298/aadm1701108a