On Gonality-Related Graph Parameters

2021 ◽  
Author(s):  
Benjamin Weber
Keyword(s):  
Related Graph ◽  
Graph Parameters

scholarly journals The main vertices of a star set and related graph parameters

2021 ◽  
Vol 344 (12) ◽  
pp. 112593
Author(s):  
Milica Anđelić ◽  
Domingos M. Cardoso ◽  
Slobodan K. Simić ◽  
Zoran Stanić
Keyword(s):  
Related Graph ◽  
Graph Parameters

Fuzzy Labeling on Cycle Related Graph

2019 ◽  
Vol 7 (6) ◽  
pp. 1192-1194
Author(s):  
M.K. Pandurangan ◽  
T. Bharathi ◽  
S.Antony Vinoth
Keyword(s):  
Related Graph

scholarly journals On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 512
Author(s):  
Maryam Baghipur ◽  
Modjtaba Ghorbani ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Distance Matrix ◽  
Upper And Lower Bounds ◽  
Laplacian Eigenvalue ◽  
Signless Laplacian ◽  
Graph Parameters ◽  
Simple Connected Graph ◽  
Second Largest Eigenvalue ◽  
Reciprocal Distance Matrix

The signless Laplacian reciprocal distance matrix for a simple connected graph G is defined as RQ(G)=diag(RH(G))+RD(G). Here, RD(G) is the Harary matrix (also called reciprocal distance matrix) while diag(RH(G)) represents the diagonal matrix of the total reciprocal distance vertices. In the present work, some upper and lower bounds for the second-largest eigenvalue of the signless Laplacian reciprocal distance matrix of graphs in terms of various graph parameters are investigated. Besides, all graphs attaining these new bounds are characterized. Additionally, it is inferred that among all connected graphs with n vertices, the complete graph Kn and the graph Kn−e obtained from Kn by deleting an edge e have the maximum second-largest signless Laplacian reciprocal distance eigenvalue.

scholarly journals From the Quasi-Total Strong Differential to Quasi-Total Italian Domination in Graphs

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1036
Author(s):  
Abel Cabrera Martínez ◽  
Alejandro Estrada-Moreno ◽  
Juan Alberto Rodríguez-Velázquez
Keyword(s):  
Vertex Cover ◽  
Domination Number ◽  
Theoretical Computer Science ◽  
Discrete Mathematics ◽  
Special Issue ◽  
Total Domination Number ◽  
Theoretical Computer ◽  
Graph Parameters ◽  
Semitotal Domination ◽  
Domination In Graphs

This paper is devoted to the study of the quasi-total strong differential of a graph, and it is a contribution to the Special Issue “Theoretical computer science and discrete mathematics” of Symmetry. Given a vertex x∈V(G) of a graph G, the neighbourhood of x is denoted by N(x). The neighbourhood of a set X⊆V(G) is defined to be N(X)=⋃x∈XN(x), while the external neighbourhood of X is defined to be Ne(X)=N(X)∖X. Now, for every set X⊆V(G) and every vertex x∈X, the external private neighbourhood of x with respect to X is defined as the set Pe(x,X)={y∈V(G)∖X:N(y)∩X={x}}. Let Xw={x∈X:Pe(x,X)≠⌀}. The strong differential of X is defined to be ∂s(X)=|Ne(X)|−|Xw|, while the quasi-total strong differential of G is defined to be ∂s*(G)=max{∂s(X):X⊆V(G)andXw⊆N(X)}. We show that the quasi-total strong differential is closely related to several graph parameters, including the domination number, the total domination number, the 2-domination number, the vertex cover number, the semitotal domination number, the strong differential, and the quasi-total Italian domination number. As a consequence of the study, we show that the problem of finding the quasi-total strong differential of a graph is NP-hard.

Homology of the line graph and of related graph-valued functions

1991 ◽  
Vol 56 (4) ◽  
pp. 400-404 ◽  
Author(s):  
Erich Prisner
Keyword(s):  
Line Graph ◽  
Related Graph

scholarly journals On the relation between a graph code and a graph state

2016 ◽  
Vol 16 (3&4) ◽  
pp. 237-250
Author(s):  
Yongsoo Hwang ◽  
Jun Heo
Keyword(s):  
Simple Graph ◽  
Graph State ◽  
Stabilizer Codes ◽  
Logical Qubits ◽  
Related Graph ◽  
Local Complementation ◽  
Stabilizer Group

A graph state and a graph code respectively are defined based on a mathematical simple graph. In this work, we examine a relation between a graph state and a graph code both obtained from the same graph, and show that a graph state is a superposition of logical qubits of the related graph code. By using the relation, we first discuss that a local complementation which has been used for a graph state can be useful for searching locally equivalent stabilizer codes, and second provide a method to find a stabilizer group of a graph code.

scholarly journals Cubical coloring — fractional covering by cuts and semidefinite programming

2015 ◽  
Vol Vol. 17 no.2 (Graph Theory) ◽  
Author(s):  
Robert Šámal
Keyword(s):  
Semidefinite Programming ◽  
Chromatic Number ◽  
Fractional Chromatic Number ◽  
Maximum Cut ◽  
Continuous Mappings ◽  
Polynomial Time Approximation Algorithm ◽  
Eigenvalue Bound ◽  
International Audience ◽  
Graph Parameters ◽  
Fractional Covering

International audience We introduce a new graph parameter that measures fractional covering of a graph by cuts. Besides being interesting in its own right, it is useful for study of homomorphisms and tension-continuous mappings. We study the relations with chromatic number, bipartite density, and other graph parameters. We find the value of our parameter for a family of graphs based on hypercubes. These graphs play for our parameter the role that cliques play for the chromatic number and Kneser graphs for the fractional chromatic number. The fact that the defined parameter attains on these graphs the correct value suggests that our definition is a natural one. In the proof we use the eigenvalue bound for maximum cut and a recent result of Engström, Färnqvist, Jonsson, and Thapper [An approximability-related parameter on graphs – properties and applications, DMTCS vol. 17:1, 2015, 33–66]. We also provide a polynomial time approximation algorithm based on semidefinite programming and in particular on vector chromatic number (defined by Karger, Motwani and Sudan [Approximate graph coloring by semidefinite programming, J. ACM 45 (1998), no. 2, 246–265]).

Sign in / Sign up

Export Citation Format

Share Document