scholarly journals The determinant of an antiadjacency matrix of a directed cycle graph with chords

2017 ◽  
Author(s):  
D. Diwyacitta ◽  
A. P. Putra ◽  
K. A. Sugeng ◽  
S. Utama
Keyword(s):  
Directed Cycle ◽  
Cycle Graph

scholarly journals The Square of a Directed Graph

2019 ◽  
Vol 8 (4) ◽  
pp. 8331-8335
Keyword(s):  
Directed Graph ◽  
Oriented Graph ◽  
Directed Cycle ◽  
Directed Path ◽  
The Relationship ◽  
Special Case ◽  
Cycle Graph

The square of an oriented graph is an oriented graph such that if and only if for some , both and exist. According to the square of oriented graph conjecture (SOGC), there exists a vertex such that . It is a special case of a more general Seymour’s second neighborhood conjecture (SSNC) which states for every oriented graph , there exists a vertex such that . In this study, the methods to square a directed graph and verify its correctness were introduced. Moreover, some lemmas were introduced to prove some classes of oriented graph including regular oriented graph, directed cycle graph and directed path graphs are satisfied the SOGC. Besides that, the relationship between SOGC and SSNC are also proved in this study. As a result, the verification of the SOGC in turn implies partial results for SSNC.

Packing coloring on subdivision-vertex and subdivision-edge join of cycle Cm with path Pn

2020 ◽  
pp. 627-634
Author(s):  
K. Rajalakshmi ◽  
M. Venkatachalam ◽  
M. Barani ◽  
D. Dafik
Keyword(s):  
Chromatic Number ◽  
Path Graph ◽  
Packing Chromatic Number ◽  
Cycle Graph

The packing chromatic number $\chi_\rho$ of a graph $G$ is the smallest integer $k$ for which there exists a mapping $\pi$ from $V(G)$ to $\{1,2,...,k\}$ such that any two vertices of color $i$ are at distance at least $i+1$. In this paper, the authors find the packing chromatic number of subdivision vertex join of cycle graph with path graph and subdivision edge join of cycle graph with path graph.

scholarly journals Linkedness and Ordered Cycles in Digraphs

2008 ◽  
Vol 17 (3) ◽  
pp. 411-422 ◽  
Author(s):  
DANIELA KÜHN ◽  
DERYK OSTHUS
Keyword(s):  
Directed Cycle

Given a digraphD, let δ0(D) := min{δ+(D), δ−(D)} be the minimum semi-degree ofD. We show that every sufficiently large digraphDwith δ0(D)≥n/2 +l−1 isl-linked. The bound on the minimum semi-degree is best possible and confirms a conjecture of Manoussakis [17]. We also determine the smallest minimum semi-degree which ensures that a sufficiently large digraphDisk-ordered,i.e., that for every sequences1, . . .,skof distinct vertices ofDthere is a directed cycle which encounterss1, . . .,skin this order. This result will be used in [16].

scholarly journals Graph splicing rules with cycle graph and its complement on complete graphs

2021 ◽  
Vol 1988 (1) ◽  
pp. 012067
Author(s):  
M N S Abdul Razak ◽  
W H Fong ◽  
N H Sarmin
Keyword(s):  
Complete Graphs ◽  
Cycle Graph

scholarly journals The Three Colour Hat Guessing Game on Cycle Graphs

10.37236/5135 ◽  
2017 ◽  
Vol 24 (1) ◽  
Author(s):  
Witold Szczechla
Keyword(s):  
Incomplete Information ◽  
Cooperative Game ◽  
Winning Strategy ◽  
Relational System ◽  
Asymmetric Game ◽  
Cycle Graph

We study a cooperative game in which each member of a team of N players, wearing coloured hats and situated at the vertices of the cycle graph with N vertices, is guessing their own hat colour merely on the basis of observing the hats worn by their two neighbours without exchanging the information. Each hat can have one of three colours. A predetermined guessing strategy is winning if it guarantees at least one correct individual guess for every assignment of colours. We prove that a winning strategy exists if and only if N is divisible by 3 or N = 4. This asymmetric game is an example of relational system using incomplete information about an unpredictable situation, where at least one participant has to act properly.

scholarly journals Graph energy change due to any single edge deletion

2015 ◽  
Vol 29 ◽  
pp. 59-73
Author(s):  
Wen-Huan Wang ◽  
Wasin So
Keyword(s):  
Partial Solution ◽  
Energy Change ◽  
Single Edge ◽  
Edge Deletion ◽  
Numerical Evidence ◽  
Graph Energy ◽  
The Absolute ◽  
Cycle Graph

The energy of a graph is the sum of the absolute values of its eigenvalues. We propose a new problem on graph energy change due to any single edge deletion. Then we survey the literature for existing partial solution of the problem, and mention a conjecture based on numerical evidence. Moreover, we prove in three different ways that the energy of a cycle graph decreases when an arbitrary edge is deleted except for the order of 4.

Sign in / Sign up

Export Citation Format

Share Document