Temat: ladder graph - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: Rank numbers for bent ladders
Autorzy:: Richter, Peter
Leven, Emily
Tran, Anh
Ek, Bryan
Jacob, Jobby
Narayan, Darren A.
Tematy:: graph colorings
rankings of graphs
rank number
Cartesian product of graphs
ladder graph
bent ladder graph; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/30148235.pdf Link otwiera się w nowym oknie
Opis:: A ranking on a graph is an assignment of positive integers to its vertices such that any path between two vertices with the same label contains a vertex with a larger label. The rank number of a graph is the fewest number of labels that can be used in a ranking. The rank number of a graph is known for many families, including the ladder graph $P_2 × P_n$. We consider how ”bending” a ladder affects the rank number. We prove that in certain cases the rank number does not change, and in others the rank number differs by only 1. We investigate the rank number of a ladder with an arbitrary number of bends
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Strong incidence colouring of graphs
Autorzy:: Benmedjdoub, Brahim
Sopena, Éric
Tematy:: strong incidence colouring
incidence colouring
tree
Halin graph
ladder graph
square grids
necklace
double star
wheel graph; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/59896529.pdf Link otwiera się w nowym oknie
Opis:: An incidence of a graph $G$ is a pair $(v,e)$ where $v$ is a vertex of $G$ and $e$ is an edge of $G$ incident with $v$. Two incidences $(v,e)$ and $(w,f)$ of $G$ are adjacent whenever (i) $v=w$, or (ii) $e=f$, or (iii) $vw=e$ or $f$. An incidence $p$-colouring of $G$ is a mapping from the set of incidences of $G$ to the set of colours $\{1, . . . , p\}$ such that every two adjacent incidences receive distinct colours. Incidence colouring has been introduced by Brualdi and Quinn Massey in 1993 and, since then, studied by several authors. In this paper, we introduce and study the strong version of incidence colouring, where incidences adjacent to the same incidence must also get distinct colours. We determine the exact value of — or upper bounds on — the strong incidence chromatic number of several classes of graphs, namely cycles, wheel graphs, trees, ladder graphs, square grids and subclasses of Halin graphs.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: On super (a,d)-edge antimagic total labeling of certain families of graphs
Autorzy:: Roushini Leely Pushpam, P.
Saibulla, A.
Tematy:: edge weight
magic labeling
antimagic labeling
ladder
fan graph
prism and web graph; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/743252.pdf Link otwiera się w nowym oknie
Opis:: A (p, q)-graph G is (a,d)-edge antimagic total if there exists a bijection f: V(G) ∪ E(G) → {1, 2,...,p + q} such that the edge weights Λ(uv) = f(u) + f(uv) + f(v), uv ∈ E(G) form an arithmetic progression with first term a and common difference d. It is said to be a super (a, d)-edge antimagic total if the vertex labels are {1, 2,..., p} and the edge labels are {p + 1, p + 2,...,p + q}. In this paper, we study the super (a,d)-edge antimagic total labeling of special classes of graphs derived from copies of generalized ladder, fan, generalized prism and web graph.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: On Edge H-Irregularity Strengths of Some Graphs
Autorzy:: Naeem, Muhammad
Siddiqui, Muhammad Kamran
Bača, Martin
Semaničová-Feňovčíková, Andrea
Ashraf, Faraha
Tematy:: prism
antiprism
triangular ladder
diagonal ladder
wheel
gear graph
H-irregular edge labeling
edge H-irregularity strength; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/32225869.pdf Link otwiera się w nowym oknie
Opis:: For a graph G an edge-covering of G is a family of subgraphs H₁, H₂, . . ., H_t such that each edge of E(G) belongs to at least one of the subgraphs H_i, i = 1, 2, . . ., t. In this case we say that G admits an (H₁, H₂, . . ., H_t)-(edge) covering. An H-covering of graph G is an (H₁, H₂, . . ., H_t)-(edge) covering in which every subgraph H_i is isomorphic to a given graph H. Let G be a graph admitting H-covering. An edge k-labeling α : E(G) → {1, 2, . . ., k} is called an H-irregular edge k-labeling of the graph G if for every two different subgraphs H′ and H′′ isomorphic to H their weights wt_α(H′) and wt_α(H′″) are distinct. The weight of a subgraph H under an edge k-labeling is the sum of labels of edges belonging to H. The edge H-irregularity strength of a graph G, denoted by ehs(G, H), is the smallest integer k such that G has an H-irregular edge k-labeling. In this paper we determine the exact values of ehs(G, H) for prisms, antiprisms, triangular ladders, diagonal ladders, wheels and gear graphs. Moreover the subgraph H is isomorphic to only C₄, C₃ and K₄.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: Metoda reprezentacji pośredniej programu PLC opisanego za pomocą języków LD i SFC na potrzeby syntezy sprzętowej
A common intermediate representation of LD and SFC programs for hardware synthesis purposes
Autorzy:: Milik, A.
Tematy:: sterownik programowalny
diagram stykowy
LD
sekwencyjny schemat funkcji
SFC
synteza logiczna wysokiego poziomu
graf przepływu danych
DFG
FPGA
układy rekonfigurowane
PLC
high level logic synthesis
DFG (data flow graph)
data flow graph
ladder diagram; Pokaż więcej
Wydawca:: Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Powiązania:: https://bibliotekanauki.pl/articles/151128.pdf Link otwiera się w nowym oknie
Opis:: W artykule przedstawiono metody reprezentacji pośredniej programu sterowania opisanego językiem LD oraz SFC zgodnie z IEC61131-3, opracowane na potrzeby syntezy sprzętowej kładów sterowania PLC implementowanych w strukturach programowalnych FPGA. W opisie wykorzystano oryginalną implementację grafu skierowanego. Przedstawiono opracowane reguły odwzorowania, zapewniające zachowanie zależności sekwencyjnych przy jednoczesnym uzyskaniu maksymalnego zrównoleglenia działania. Przedstawiono również zarys metod syntezy na podstawie opracowanego odwzorowania pośredniego.
The increased performance of a PLC can be achieved by direct implementation of a control program in an FPGA device [3, 6, 7, 8, 12, 13]. The paper presents a methodology of transforming a standard PLC program given by LD or SFC according to IEC61131-3 to the common intermediate form dedicated for logic synthesis. The intermediate form of the control program is represented by a data flow graph (DFG, Fig. 1). The set of nodes is carefully selected to minimize the number of different types of nodes while assuring implementation of PLC behavior. Attributed edges and multiple argument nodes are used to reduce size of DFG (Fig. 2). The developed method for creating a DAG maintains sequential dependencies between variables and revel operations parallelism. In PLC programs the variables pass values between operations and computation cycles. In order to maintain sequential dependencies, value assignment to a variable is observed. If the accessed variable has not been assigned, its value is used for a driving node (Fig. 3). The SFC is based on step, actions and transitions [2]. The step variable in the DFG is represented by a JK flip-flop equivalent. The activation function of a step is based on analysis of its dependencies with preceding and succeeding steps and transitions (Fig. 5). Actions that are bounded with steps are controlled according to their types (Fig. 6). The presented intermediated representation has been successfully applied to synthesize a PLC implemented in an FPGA device.
Dostawca treści:: Biblioteka Nauki

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