Geodetic Number Of Circulant Graphs Cm({2,4,...,⌊m⌋−1,⌊m⌋})

2021 ◽  
Vol 15 (2) ◽  
pp. 165-169
Keyword(s):  
Circulant Graphs ◽  
Geodetic Number

scholarly journals Algorithmic upper bounds for graph geodetic number

2021 ◽  
Author(s):  
Ahmad T. Anaqreh ◽  
Boglárka G.-Tóth ◽  
Tamás Vinkó
Keyword(s):  
Upper Bounds ◽  
Geodetic Number

scholarly journals The energy of integral circulant graphs with prime power order

2011 ◽  
Vol 5 (1) ◽  
pp. 22-36 ◽  
Author(s):  
J.W. Sander ◽  
T. Sander
Keyword(s):  
Adjacency Matrix ◽  
Prime Power ◽  
Prime Power Order ◽  
Circulant Graph ◽  
Closed Formula ◽  
Circulant Graphs ◽  
Vertex Set

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. Such a graph can be characterized by its vertex count n and a set D of divisors of n such that its vertex set is Zn and its edge set is {{a,b} : a, b ? Zn; gcd(a-b, n)? D}. For an integral circulant graph on ps vertices, where p is a prime, we derive a closed formula for its energy in terms of n and D. Moreover, we study minimal and maximal energies for fixed ps and varying divisor sets D.

scholarly journals Some star extremal circulant graphs

2003 ◽  
Vol 271 (1-3) ◽  
pp. 169-177 ◽  
Author(s):  
Wensong Lin
Keyword(s):  
Circulant Graphs

Kernel in Oriented Circulant Graphs

2009 ◽  
pp. 396-407 ◽  
Author(s):  
Paul Manuel ◽  
Indra Rajasingh ◽  
Bharati Rajan ◽  
Joice Punitha
Keyword(s):  
Circulant Graphs

scholarly journals Cycle Embedding in Generalized Recursive Circulant Graphs

2018 ◽  
Vol E101.D (12) ◽  
pp. 2916-2921
Author(s):  
Shyue-Ming TANG ◽  
Yue-Li WANG ◽  
Chien-Yi LI ◽  
Jou-Ming CHANG
Keyword(s):  
Circulant Graphs

scholarly journals Stability of circulant graphs

2019 ◽  
Vol 136 ◽  
pp. 154-169 ◽  
Author(s):  
Yan-Li Qin ◽  
Binzhou Xia ◽  
Sanming Zhou
Keyword(s):  
Circulant Graphs

HAMILTONIAN PROPERTIES OF FAULTY RECURSIVE CIRCULANT GRAPHS

2002 ◽  
Vol 03 (03n04) ◽  
pp. 273-289 ◽  
Author(s):  
CHANG-HSIUNG TSAI ◽  
JIMMY J. M. TAN ◽  
YEN-CHU CHUANG ◽  
LIH-HSING HSU
Keyword(s):  
Bipartite Graph ◽  
Hamiltonian Path ◽  
Circulant Graph ◽  
Circulant Graphs ◽  
Vertex Set ◽  
Regular Node ◽  
Hamiltonian Properties

We present some results concerning hamiltonian properties of recursive circulant graphs in the presence of faulty vertices and/or edges. The recursive circulant graph G(N, d) with d ≥ 2 has vertex set V(G) = {0, 1, …, N - 1} and the edge set E(G) = {(v, w)| ∃ i, 0 ≤ i ≤ ⌈ log d N⌉ - 1, such that v = w + di (mod N)}. When N = cdk where d ≥ 2 and 2 ≤ c ≤ d, G(cdk, d) is regular, node symmetric and can be recursively constructed. G(cdk, d) is a bipartite graph if and only if c is even and d is odd. Let F, the faulty set, be a subset of V(G(cdk, d)) ∪ E(G(cdk, d)). In this paper, we prove that G(cdk, d) - F remains hamiltonian if |F| ≤ deg (G(cdk, d)) - 2 and G(cdk, d) is not bipartite. Moreover, if |F| ≤ deg (G(cdk, d)) - 3 and G(cdk, d) is not a bipartite graph, we prove a more stronger result that for any two vertices u and v in V(G(cdk, d)) - F, there exists a hamiltonian path of G(cdk, d) - F joining u and v.

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