scholarly journals Closed Neighborhood Ideals of Finite Simple Graphs

La Matematica ◽  
2021 ◽  
Author(s):  
Jacob Honeycutt ◽  
Keri Sather-Wagstaff
Keyword(s):  
Simple Graphs ◽  
Closed Neighborhood

Super Graceful Labeling for Some Simple Graphs

2012 ◽  
Vol 2 (1) ◽  
pp. 35 ◽  
Author(s):  
M. A. Perumal ◽  
S. Navaneethakrishnan ◽  
A. Nagaraja ◽  
S. Arockiaraj
Keyword(s):  
Graceful Labeling ◽  
Simple Graphs

Design Criteria for Safer Manual Lifting by Men and Women

1982 ◽  
Vol 26 (6) ◽  
pp. 503-507
Author(s):  
Dudley G. Letbetter
Keyword(s):  
Muscle Fatigue ◽  
Material Handling ◽  
Human Anatomy ◽  
Design Criteria ◽  
Maximum Weight ◽  
Manual Lifting ◽  
Men And Women ◽  
Simple Graphs ◽  
Cardiovascular Capacity ◽  
Specific Material

Simplified design criteria are provided for two-handed, manual lifting by standing men and women, without selective assignment of personnel to specific material handling tasks. Based on a 1981 NIOSH report, application of these criteria requires no knowledge of human anatomy, anthropometry, biomechanics, psychophysics, muscle fatigue, cardiovascular capacity, or metabolic endurance. A person who can read and use simple graphs can quickly determine the maximum weight of a lifted object. The information needed is the horizontal grasp distance and the initial grasp height and lift distance of the object, plus the frequency and duration of lifting.

Zero-Divisor Semigroups and Some Simple Graphs

2006 ◽  
Vol 34 (8) ◽  
pp. 3043-3052 ◽  
Author(s):  
Tongsuo Wu ◽  
Dancheng Lu
Keyword(s):  
Zero Divisor ◽  
Simple Graphs

Graphs with the second signless Laplacian eigenvalue ≤ 4

2021 ◽  
Vol 10 (1) ◽  
pp. 131-152
Author(s):  
Stephen Drury
Keyword(s):  
General Solution ◽  
Knapsack Problem ◽  
Laplacian Eigenvalue ◽  
Simple Graphs ◽  
Largest Eigenvalue ◽  
Signless Laplacian ◽  
Second Largest Eigenvalue

Abstract We discuss the question of classifying the connected simple graphs H for which the second largest eigenvalue of the signless Laplacian Q(H) is ≤ 4. We discover that the question is inextricable linked to a knapsack problem with infinitely many allowed weights. We take the first few steps towards the general solution. We prove that this class of graphs is minor closed.

Fuzzy magic labeling of simple graphs

2018 ◽  
Vol 60 (1-2) ◽  
pp. 369-385
Author(s):  
M. Fathalian ◽  
R. A. Borzooei ◽  
M. Hamidi
Keyword(s):  
Simple Graphs

scholarly journals Lower Bounds for the Average Genus of a CF-graph

10.37236/422 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Yichao Chen
Keyword(s):  
Lower Bound ◽  
Linear Function ◽  
Lower Bounds ◽  
Betti Number ◽  
Maximum Genus ◽  
Simple Graphs ◽  
Structure Theorems ◽  
Average Genus

CF-graphs form a class of multigraphs that contains all simple graphs. We prove a lower bound for the average genus of a CF-graph which is a linear function of its Betti number. A lower bound for average genus in terms of the maximum genus and some structure theorems for graphs with a given average genus are also provided.

scholarly journals Densities of Minor-Closed Graph Families

10.37236/408 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
David Eppstein
Keyword(s):  
Order Type ◽  
Closed Graph ◽  
Simple Graphs ◽  
Minimal Graphs ◽  
Vertex Graph ◽  
Graph Families ◽  
A Minor ◽  
Cluster Points

We define the limiting density of a minor-closed family of simple graphs $\mathcal{F}$ to be the smallest number $k$ such that every $n$-vertex graph in $\mathcal{F}$ has at most $kn(1+o(1))$ edges, and we investigate the set of numbers that can be limiting densities. This set of numbers is countable, well-ordered, and closed; its order type is at least $\omega^\omega$. It is the closure of the set of densities of density-minimal graphs, graphs for which no minor has a greater ratio of edges to vertices. By analyzing density-minimal graphs of low densities, we find all limiting densities up to the first two cluster points of the set of limiting densities, $1$ and $3/2$. For multigraphs, the only possible limiting densities are the integers and the superparticular ratios $i/(i+1)$.

scholarly journals Another H-super magic decompositions of the lexicographic product of graphs

2018 ◽  
Vol 2 (2) ◽  
pp. 72
Author(s):  
H Hendy ◽  
Kiki A. Sugeng ◽  
A.N.M Salman ◽  
Nisa Ayunda
Keyword(s):  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Graph Decomposition ◽  
Graph Labeling ◽  
Sufficient Condition ◽  
Lexicographic Product ◽  
Simple Graphs ◽  
Product Of Graphs

<p>Let <span class="math"><em>H</em></span> and <span class="math"><em>G</em></span> be two simple graphs. The concept of an <span class="math"><em>H</em></span>-magic decomposition of <span class="math"><em>G</em></span> arises from the combination between graph decomposition and graph labeling. A decomposition of a graph <span class="math"><em>G</em></span> into isomorphic copies of a graph <span class="math"><em>H</em></span> is <span class="math"><em>H</em></span>-magic if there is a bijection <span class="math"><em>f</em> : <em>V</em>(<em>G</em>) ∪ <em>E</em>(<em>G</em>) → {1, 2, ..., ∣<em>V</em>(<em>G</em>) ∪ <em>E</em>(<em>G</em>)∣}</span> such that the sum of labels of edges and vertices of each copy of <span class="math"><em>H</em></span> in the decomposition is constant. A lexicographic product of two graphs <span class="math"><em>G</em><sub>1</sub></span> and <span class="math"><em>G</em><sub>2</sub>, </span> denoted by <span class="math"><em>G</em><sub>1</sub>[<em>G</em><sub>2</sub>], </span> is a graph which arises from <span class="math"><em>G</em><sub>1</sub></span> by replacing each vertex of <span class="math"><em>G</em><sub>1</sub></span> by a copy of the <span class="math"><em>G</em><sub>2</sub></span> and each edge of <span class="math"><em>G</em><sub>1</sub></span> by all edges of the complete bipartite graph <span class="math"><em>K</em><sub><em>n</em>, <em>n</em></sub></span> where <span class="math"><em>n</em></span> is the order of <span class="math"><em>G</em><sub>2</sub>.</span> In this paper we provide a sufficient condition for <span class="math">$\overline{C_{n}}[\overline{K_{m}}]$</span> in order to have a <span class="math">$P_{t}[\overline{K_{m}}]$</span>-magic decompositions, where <span class="math"><em>n</em> &gt; 3, <em>m</em> &gt; 1, </span> and <span class="math"><em>t</em> = 3, 4, <em>n</em> − 2</span>.</p>

scholarly journals Lower Bounds for Identifying Codes in some Infinite Grids

10.37236/394 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Ryan Martin ◽  
Brendon Stanton
Keyword(s):  
Lower Bounds ◽  
Finite Graph ◽  
Infinite Graphs ◽  
Locally Finite ◽  
Identifying Codes ◽  
Identifying Code ◽  
Hexagonal Grids ◽  
Closed Neighborhood ◽  
Definition Of ◽  
Infinite Grids

An $r$-identifying code on a graph $G$ is a set $C\subset V(G)$ such that for every vertex in $V(G)$, the intersection of the radius-$r$ closed neighborhood with $C$ is nonempty and unique. On a finite graph, the density of a code is $|C|/|V(G)|$, which naturally extends to a definition of density in certain infinite graphs which are locally finite. We present new lower bounds for densities of codes for some small values of $r$ in both the square and hexagonal grids.

scholarly journals Spaces for which the diagonal has a closed neighborhood base

1987 ◽  
Vol 53 (1) ◽  
pp. 49-56 ◽  
Author(s):  
Klaas Pieter Hart
Keyword(s):  
Neighborhood Base ◽  
Closed Neighborhood
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