نتایج جستجو برای: integral graphs

تعداد نتایج: 211307  

Journal: :Publikacije Elektrotehnickog fakulteta - serija: matematika 2002

Journal: :Applied Mathematics and Computation 2011
Aleksandar Ilic Milan Basic

Circulant graphs are an important class of interconnection networks in parallel and distributed computing. Integral circulant graphs play an important role in modeling quantum spin networks supporting the perfect state transfer as well. The integral circulant graph ICGn(D) has the vertex set Zn = {0, 1, 2, . . . , n− 1} and vertices a and b are adjacent if gcd(a− b, n) ∈ D, where D ⊆ {d : d | n...

Journal: :Contributions to Discrete Mathematics 2013
Juergen Sander Torsten Sander

The energy of a graph was introduced by Gutman in 1978 as the sum of the absolute values of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs. These are Cayley graphs on cyclic groups (i.e. there adjacency matrix is circulant) each of whose eigenvalues is an integer. Given an arbitrary prime power p, we determine all integral circu...

Journal: :Linear Algebra and its Applications 2023

A mixed graph is said to be second kind hermitian integral (HS-integral) if the eigenvalues of its Hermitian-adjacency matrix are integers. called Eisenstein (0, 1)-adjacency We characterize set S for which normal Cayley Cay(Γ,S) HS-integral any finite group Γ. further show that a and only it integral. This paper generalizes results Kadyan Bhattacharjy (2022) [11].

Journal: :EJGTA 2016
Chandrashekar Adiga B. R. Rakshith K. N. Subba Krishna

In this paper we define extended corona and extended neighborhood corona of two graphs G1 and G2, which are denoted by G1 • G2 and G1 ∗ G2 respectively. We compute their adjacency spectrum, Laplacian spectrum and signless Laplacian spectrum. As applications, we give methods to construct infinite families of integral graphs, Laplacian integral graphs and expander graphs from known ones.

1997
Jer-Jeong Chen Gerard J. Chang Kuo-Ching Huang

Suppose D is a subset of all positive integers. The distance graph G(Z,D) with distance set D is the graph with vertex set Z, and two vertices x and y are adjacent if and only if |x− y| ∈ D. This paper studies the chromatic number χ(Z,D) of G(Z,D). In particular, we prove that χ(Z,D) ≤ |D|+1 when |D| is finite. Exact values of χ(G,D) are also determined for some D with |D| = 3. c © 1997 John Wi...

2007
Pierre Hansen Hadrien Mélot Dragan Stevanović

We give characterizations of integral graphs in the family of complete split graphs and a few related families of graphs.

Journal: :Electr. J. Comb. 2009
Torsten Sander

Sudoku graphs have only 5 or 6 distinct eigenvalues and all of them are integers. Moreover, the associated eigenspaces admit bases with entries from the set {0, 1,−1}.

Journal: :Discrete Mathematics 2002
Leonid S. Melnikov Artem V. Pyatkin

Given a set of integers S; G(S) = (S; E) is a graph, where the edge uv exists if and only if u+ v∈ S. A graph G = (V; E) is an integral sum graph or ISG if there exists a set S ⊂ Z such that G=G(S). This set is called a labeling of G. The main results of this paper concern regular ISGs. It is proved that all 2-regular graphs with the exception of C4 are integral sum graphs and that for every po...

Journal: :Discrete Mathematics 2008
Ligong Wang Xiaodong Liu

A graph is called integral if all eigenvalues of its adjacency matrix are integers. In this paper, we investigate integral complete r-partite graphsKp1,p2,...,pr =Ka1·p1,a2·p2,...,as ·ps with s=3, 4.We can construct infinite many new classes of such integral graphs by solving some certain Diophantine equations. These results are different from those in the existing literature. For s = 4, we giv...

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