A Little Simple Graph Theory

1999 ◽  
pp. 17-24
Author(s):  
Gilbert G. Walter ◽  
Martha Contreras
Keyword(s):  
Graph Theory ◽  
Simple Graph

scholarly journals Nordhaus–Gaddum-Type Relations for Arithmetic-Geometric Spectral Radius and Energy

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yajing Wang ◽  
Yubin Gao
Keyword(s):  
Graph Theory ◽  
Spectral Radius ◽  
Adjacency Matrix ◽  
Upper Bounds ◽  
Simple Graph ◽  
Spectral Graph Theory ◽  
Extremal Graphs ◽  
Spectral Graph ◽  
Vertex Set

Spectral graph theory plays an important role in engineering. Let G be a simple graph of order n with vertex set V=v1,v2,…,vn. For vi∈V, the degree of the vertex vi, denoted by di, is the number of the vertices adjacent to vi. The arithmetic-geometric adjacency matrix AagG of G is defined as the n×n matrix whose i,j entry is equal to di+dj/2didj if the vertices vi and vj are adjacent and 0 otherwise. The arithmetic-geometric spectral radius and arithmetic-geometric energy of G are the spectral radius and energy of its arithmetic-geometric adjacency matrix, respectively. In this paper, some new upper bounds on arithmetic-geometric energy are obtained. In addition, we present the Nordhaus–Gaddum-type relations for arithmetic-geometric spectral radius and arithmetic-geometric energy and characterize corresponding extremal graphs.

scholarly journals Medicinal cupping in the eyes of graph theory

2020 ◽  
Vol 1 (01) ◽  
pp. 44-49
Author(s):  
N.M Hanafi ◽  
Y. Yusof ◽  
M.S. Mohamad ◽  
M.F.A Bakar ◽  
M.A. Ibrahim
Keyword(s):  
Graph Theory ◽  
Human Health ◽  
Healing Process ◽  
Optimal Number ◽  
Simple Graph ◽  
The Body ◽  
Graph Colouring ◽  
Traditional Treatment ◽  
The World ◽  
Definition Of

Medicinal cupping is one of the traditional treatment methods that is trusted to give many benefits to the human health and still practising by various culture and societies around the world. The purposes of this treatment are to allow the toxin leaves the body,to stimulate the muscles and also helping in healing process for various diseases. The process start by placing special heated cups on specific points to create suction, then the points will be punctured. Each disease has specific cupping points to be cupped which located on the human nerves system. All the points actually connected to each other where a simple graph can be formed. Since there are limited studies that discuss medicinal cupping in a mathematics view, thus this research is conducted to introduce the easiest way  on demonstrating the cupping points on the human nerves system by using the idea of graph. Hence, new definition of nerve vertex, nerve edge and nerve graph will be defined. Moreover, the idea of graph colouring will be applied to determine the optimal number of cupping points.

scholarly journals A variant of Niessen’s problem on degreesequences of graphs

2014 ◽  
Vol Vol. 16 no. 1 (Graph Theory) ◽  
Author(s):  
Jiyun Guo ◽  
Jianhua Yin
Keyword(s):  
Graph Theory ◽  
Discrete Math ◽  
Simple Graph ◽  
The Other ◽  
Degree Sequences ◽  
International Audience

Graph Theory International audience Let (a1,a2,\textellipsis,an) and (b1,b2,\textellipsis,bn) be two sequences of nonnegative integers satisfying the condition that b1>=b2>=...>=bn, ai<= bi for i=1,2,\textellipsis,n and ai+bi>=ai+1+bi+1 for i=1,2,\textellipsis, n-1. In this paper, we give two different conditions, one of which is sufficient and the other one necessary, for the sequences (a1,a2,\textellipsis,an) and (b1,b2,\textellipsis,bn) such that for every (c1,c2,\textellipsis,cn) with ai<=ci<=bi for i=1,2,\textellipsis,n and &#x2211;&limits;i=1n ci=0 (mod 2), there exists a simple graph G with vertices v1,v2,\textellipsis,vn such that dG(vi)=ci for i=1,2,\textellipsis,n. This is a variant of Niessen\textquoterights problem on degree sequences of graphs (Discrete Math., 191 (1998), 247&#x2013;253).

scholarly journals Graceful Labeling of Hypertrees

2021 ◽  
Vol 13 (1) ◽  
pp. 28
Author(s):  
H. El-Zohny ◽  
S. Radwan ◽  
S.I. Abo El-Fotooh ◽  
Z. Mohammed
Keyword(s):  
Graph Theory ◽  
Simple Graph ◽  
Graph Labeling ◽  
Graceful Labeling ◽  
Edge Labeling

Graph labeling is considered as one of the most interesting areas in graph theory. A labeling for a simple graph G (numbering or valuation), is an association of non -negative integers to vertices of G&nbsp; (vertex labeling) or to edges of G&nbsp; (edge labeling) or both of them. In this paper we study the graceful labeling for the k- uniform hypertree and define a condition for the corresponding tree to be graceful. A k- uniform hypertree is graceful if the minimum difference of vertices&rsquo; labels of each edge is distinct and each one is the label of the corresponding edge.

scholarly journals Detection of Sub-Community Graph in N-Community Graphs using Graph Mining

2020 ◽  
Vol 9 (3) ◽  
pp. 2014-2023
Keyword(s):  
Graph Theory ◽  
Graph Mining ◽  
Simple Graph ◽  
Important Task

Detection of sub-graphs in community graphs is an important task and useful for characterizing community graphs. This characterization leads to classification as well as clusterings of community graphs. It also leads to finding differences among a set of community graphs as well as buildings of indices of community graphs. Finally, this characterization leads discovery of knowledge from sub-graphs. This proposed approach of detection of a sub-community graph from a group of community graphs using simple graph theory techniques. So, that knowledge could be discovered from the sub-community graph detected in a set of community graphs. The proposed algorithm has been implemented with two examples including one benchmark network and observed satisfactory results.

scholarly journals A graph theoretical approach to cis/trans isomerism

2014 ◽  
Vol 79 (7) ◽  
pp. 805-813 ◽  
Author(s):  
Boris Furtula ◽  
Giorgi Lekishvili ◽  
Ivan Gutman
Keyword(s):  
Graph Theory ◽  
Electron Energy ◽  
Theoretical Approach ◽  
Adjacency Matrix ◽  
Molecular Graph ◽  
Energy Difference ◽  
Simple Graph ◽  
Total Electron ◽  
Total Electron Energy ◽  
Graph Theoretical Approach

A simple graph-theory-based model is put forward, by means of which it is possible to express the energy difference between geometrically non-equivalent forms of a conjugated polyene. This is achieved by modifying the adjacency matrix of the molecular graph, and including into it information on cis/trans constellations. The total ?-electron energy thus calculated is in excellent agreement with the enthalpies of the underlying isomers and conformers.

scholarly journals SMT Attack: Next Generation Attack on Obfuscated Circuits with Capabilities and Performance Beyond the SAT Attacks

2018 ◽  
pp. 97-122 ◽  
Author(s):  
Kimia Zamiri Azar ◽  
Hadi Mardani Kamali ◽  
Houman Homayoun ◽  
Avesta Sasan
Keyword(s):  
Graph Theory ◽  
Hold Time ◽  
Simple Graph ◽  
Next Generation ◽  
Logical Property ◽  
Satisfiability Modulo Theory ◽  
Speed Up ◽  
Sat Solver ◽  
And Performance

In this paper, we introduce the Satisfiability Modulo Theory (SMT) attack on obfuscated circuits. The proposed attack is the superset of Satisfiability (SAT) attack, with many additional features. It uses one or more theory solvers in addition to its internal SAT solver. For this reason, it is capable of modeling far more complex behaviors and could formulate much stronger attacks. In this paper, we illustrate that the use of theory solvers enables the SMT to carry attacks that are not possible by SAT formulated attacks. As an example of its capabilities, we use the SMT attack to break a recent obfuscation scheme that uses key values to alter delay properties (setup and hold time) of a circuit to remain SAT hard. Considering that the logic delay is not a Boolean logical property, the targeted obfuscation mechanism is not breakable by a SAT attack. However, in this paper, we illustrate that the proposed SMT attack, by deploying a simple graph theory solver, can model and break this obfuscation scheme in few minutes. We describe how the SMT attack could be used in one of four different attack modes: (1) We explain how SMT attack could be reduced to a SAT attack, (2) how the SMT attack could be carried out in Eager, and (3) Lazy approach, and finally (4) we introduce the Accelerated SMT (AccSMT) attack that offers significant speed-up to SAT attack. Additionally, we explain how AccSMT attack could be used as an approximate attack when facing SMT-Hard obfuscation schemes.

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