Sequences with a unique realization by simple graphs

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.

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Zero-Divisor Semigroups and Some Simple Graphs

Communications in Algebra ◽

10.1080/00927870600639948 ◽

2006 ◽

Vol 34 (8) ◽

pp. 3043-3052 ◽

Cited By ~ 10

Author(s):

Tongsuo Wu ◽

Dancheng Lu

Keyword(s):

Zero Divisor ◽

Simple Graphs

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Graphs with the second signless Laplacian eigenvalue ≤ 4

Special Matrices ◽

10.1515/spma-2021-0152 ◽

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.

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Fuzzy magic labeling of simple graphs

Journal of Applied Mathematics and Computing ◽

10.1007/s12190-018-01218-x ◽

2018 ◽

Vol 60 (1-2) ◽

pp. 369-385

Author(s):

M. Fathalian ◽

R. A. Borzooei ◽

M. Hamidi

Keyword(s):

Simple Graphs

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Lower Bounds for the Average Genus of a CF-graph

The Electronic Journal of Combinatorics ◽

10.37236/422 ◽

2010 ◽

Vol 17 (1) ◽

Cited By ~ 2

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.

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Densities of Minor-Closed Graph Families

The Electronic Journal of Combinatorics ◽

10.37236/408 ◽

2010 ◽

Vol 17 (1) ◽

Cited By ~ 6

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 $i/(i+1)$.

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

Indonesian Journal of Combinatorics ◽

10.19184/ijc.2018.2.2.2 ◽

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

Let H and G be two simple graphs. The concept of an H-magic decomposition of G arises from the combination between graph decomposition and graph labeling. A decomposition of a graph G into isomorphic copies of a graph H is H-magic if there is a bijection f : V(G) ∪ E(G) → {1, 2, ..., ∣V(G) ∪ E(G)∣} such that the sum of labels of edges and vertices of each copy of H in the decomposition is constant. A lexicographic product of two graphs G1 and G2, denoted by G1[G2], is a graph which arises from G1 by replacing each vertex of G1 by a copy of the G2 and each edge of G1 by all edges of the complete bipartite graph Kn, n where n is the order of G2. In this paper we provide a sufficient condition for $\overline{C_{n}}[\overline{K_{m}}]$ in order to have a $P_{t}[\overline{K_{m}}]$-magic decompositions, where n > 3, m > 1, and t = 3, 4, n − 2.

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