The energy of integral circulant graphs with prime power order
نویسندگان
چکیده
منابع مشابه
Integral circulant graphs of prime power order with maximal energy
The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs, which can be characterized by their vertex count n and a set D of divisors of n in such a way that they have vertex set Zn and edge set {{a, b} : a, b ∈ Zn, gcd(a− b, n) ∈ D}. Using tools from convex optimization, we study the maxim...
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A connected ρ-regular graph G has largest eigenvalue ρ in modulus. G is called Ramanujan if it has at least 3 vertices and the second largest modulus of its eigenvalues is at most 2 √ ρ− 1. In 2010 Droll classified all Ramanujan unitary Cayley graphs. These graphs of type ICG(n, {1}) form a subset of the class of integral circulant graphs ICG(n,D), which can be characterised by their order n an...
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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...
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a graph is called textit{circulant} if it is a cayley graph on a cyclic group, i.e. its adjacency matrix is circulant. let $d$ be a set of positive, proper divisors of the integer $n>1$. the integral circulant graph $icg_{n}(d)$ has the vertex set $mathbb{z}_{n}$ and the edge set e$(icg_{n}(d))= {{a,b}; gcd(a-b,n)in d }$. let $n=p_{1}p_{2}cdots p_{k}m$, where $p_{1},p_{2},cdots,p_{k}$ are disti...
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ژورنال
عنوان ژورنال: Applicable Analysis and Discrete Mathematics
سال: 2011
ISSN: 1452-8630,2406-100X
DOI: 10.2298/aadm110131003s