Fast Graph Simplification for Interleaved-Dyck Reachability

Assigning an integer to a vertices or edges is called a vertex or edge labeling respectively. Suppose G is a simple graph. Consider the function f for the edge set . For each vertex t , define f(t)= (mod2). The function f is known as an E-cordial labeling (E-CL) of G if , and where , and , are the number of edges and vertices labeled with 0 and labeled by 1 respectively. A graph that admits E-CL is said to be E-cordial graphs (E-CG). Based on the above definition we propose a novel labeling known as SP Mean E-cordial labeling (E-CL). In this paper, we study SP Mean E-CL of several families of graphs such as complete bipartite graphs, complete graphs, wheels, etc.

Let G be a simple graph with vertex set V(G) and edge set E(G). Let ⟨ℤ2, +,*⟩ be a field with two elements. A vertex labeling f : V(G) → ℤ2 induces two edge labelings f+: E(G) → ℤ2 such that f+ (xy) = f(x) + f(y), whereas f* : E(G) → ℤ2 such that f* (xy) = f(x) f(y), for each edge xy ∈ E(G). For i ϵ ℤ2, let and . A labeling f of a graph G is said to be friendly if |υf (0) −υf (1)|≤ 1. The friendly index set of the graph G, denoted FI(G), is defined as the vertex labeling f is friendly}. This is a generalization of graph cordiality. The corresponding multiplicative version is called the product-cordial index set, denoted PCI(G), defined as the vertex labeling f is friendly}. In this paper, we investigate the friendly index and product-cordial index sets of a family of cubic graphs known as Möbius-liked graph, MG(n) for even n ≥ 4.

The computational complexity of cordial and equitable labelling

Let G=(V,E) be a simple graph. A vertex labeling f:V(G)→{1,2,⋯,k} is defined to be a local inclusive (respectively, non-inclusive) d-distance vertex irregular labeling of a graph G if for any two adjacent vertices x,y∈V(G) their weights are distinct, where the weight of a vertex x∈V(G) is the sum of all labels of vertices whose distance from x is at most d (respectively, at most d but at least 1). The minimum k for which there exists a local inclusive (respectively, non-inclusive) d-distance vertex irregular labeling of G is called the local inclusive (respectively, non-inclusive) d-distance vertex irregularity strength of G. In this paper, we present several basic results on the local inclusive d-distance vertex irregularity strength for d=1 and determine the precise values of the corresponding graph invariant for certain families of graphs.

Let G be a simple graph, let f : V(G)&#8594{1,2,...,|V(G)|} be a bijective mapping. The weight of v &#8712 V(G) is the sum of labels of all vertices adjacent to v . We say that f is a distance magic labeling of G if the weight of every vertex is the same constant k and we say that f is a handicap magic labeling of G if the weight of every vertex v is l + f(v) for some constant l. Graphs that allow such labelings are called distance magic or handicap, respectively. Distance magic and handicap labelings of regular graphs are used for scheduling incomplete tournaments. While distance magic labelings correspond to so called equalized tournaments, handicap labelings can be used to schedule incomplete tournaments that are more challenging to stronger teams or players, hence they increase competition and yield attractive schemes in which every games counts. We summarize known results on distance magic and handicap labelings and construct a new infinite class of 4-regular handicap graphs.

Let G = (V,E) be a simple graph. L(2, 1)−labeling defined as a functionf : V (G) → N0 such that, x and y are two adjacent vertices in V, then if x andy are adjacent to each other, |f(y) − f(x)| ≥ 2 and if x and y have the distance 2,|f(y) − f(x)| ≥ 1. The L(2, 1)-labeling number of G, called λ2,1(G), is the smallestnumbermof G. In this paper, we will further discuss the L(2, 1)-labeling of mongoliantent, lobster, triangular snake, and kayak paddle.Keywords: L(2,1)-Labeling, mongolian tent, lobster, triangular snake, kayak paddle.

This chapter investigates three special cases of monomial ideals that are important for graph theory and combinatorics: the edge ideal of a simple graph and the Stanley-Reisner and facet ideals of a simplicial complex. Each of these cases is a monomial ideal that is “square free”. These ideals are treated, in general, in Section 4.1. Graphs and their edge ideals are introduced in Section 4.2, and the decompositions of edge ideals are described in Section 4.3. Simplicial complexes and their Stanley-Reisner ideals are presented in Section 4.4, and the decompositions of Stanley-Reisner ideals are described in Section 4.5. This includes, as a consequence, a method for finding decompositions of arbitrary square-free monomial ideals. Section 4.6 treats the facet ideals associated to simplicial complexes, and their m-irreducible decompositions. The chapter ends in Section 4.7 with an exploration of Alexander duality, a process that transforms monomial generating sequences to m-irreducible decompositions, and vice versa.

A simple, connected and undirected graph with n vertices is said to have (MMD) modular multiplicative divisor labeling if there exist a one to one and on to function f from vertices of the graph to set of all natural numbers from 1 to n and label induced on the edges by the product of labels of end vertices modulo n such that addition of all edge labels is congruent to 0 (mod n). This paper studies MMD labeling of complete tripartite graphs and some open problems.

In graph theory many useful mathematical disciplines, but the extremely useful one is graph labeling. A graph labeling is used in many applications in various fields like X-ray crystallography, computer science, data base management, coding theory, astronomy and physics. A labeling of edges and vertices of a simple graph G(V, E) by a mapping ¥ : V(G) ∪ E(G) → {1, 2, 3, … , ℜ} provided that any two different edges have distinct weights is called an edge irregular total ℜ -labeling. If ℜ is minimum and G admits an edge irregular total ℜ-labeling, then it is called the total edge irregularity strength (TEIS) denoted by tes(G). In this paper, we have introduced three definitions: the quintet snake graph QS n , the double quintet snake graph D(QS n) and the m–multiple quintet snake graph M(QS n). Moreover, the exact value of TEIS for the new graphs are investigated.

A learning model is considered in terms of formal concept analysis (FCA). This model is generalized for objects represented by sets of graphs with partially ordered labels of vertices and edges (these graphs can be considered as simple conceptual graphs). An algorithm that computes all concepts and the linear (Hasse) diagram of the concept lattice in time linear with respect to the number of concepts is presented. The linear diagram gives the structure of the set of all concepts with respect to the partial order on them and provides a useful tool for browsing or discovery of implications (associations) in data.

<p>Suppose <em>G</em>(<em>V,E</em>) be a connected simple graph and suppose <em>u,v,x</em> be vertices of graph <em>G</em>. A bijection <em>f</em> : <em>V</em> ∪ <em>E</em> → {1,2,3,...,|<em>V</em> (<em>G</em>)| + |<em>E</em>(<em>G</em>)|} is called super local edge antimagic total labeling if for any adjacent edges <em>uv</em> and <em>vx</em>, <em>w</em>(<em>uv</em>) 6= <em>w</em>(<em>vx</em>), which <em>w</em>(<em>uv</em>) = <em>f</em>(<em>u</em>)+<em>f</em>(<em>uv</em>)+<em>f</em>(<em>v</em>) for every vertex <em>u,v,x</em> in <em>G</em>, and <em>f</em>(<em>u</em>) < <em>f</em>(<em>e</em>) for every vertex <em>u</em> and edge <em>e</em> ∈ <em>E</em>(<em>G</em>). Let γ(<em>G</em>) is the chromatic number of edge coloring of a graph <em>G</em>. By giving <em>G</em> a labeling of <em>f</em>, we denotes the minimum weight of edges needed in <em>G</em> as γ<em>leat</em>(<em>G</em>). If every labels for vertices is smaller than its edges, then it is be considered γ<em>sleat</em>(<em>G</em>). In this study, we proved the γ sleat of paths and its derivation.</p>

In this paper, we introduce a new type of Labeling of a graph G (V, E) with |V(G)| vertices and |E(G)| edges as an injective map φ: V(G) → {1, … . k}, k ∊ ℕ such that the induced constant mapping φ*: E(G) → (0, 1) by φ*(e) = φ*(uv) = |φ(u) - φ(v)|p = λ, where λ ∊ (0, 1) called p-adic distance labeling, for any fixed prime ‘p’. Here, we prove the existence of this new p−adic distance labeling for some simple graphs such as Path (Pn), Cycle (Cn), Complete graph (Kn) and Star graph (K1, n), n ≥ 3 also for the Corona graph Pn⊙k2¯, when n≥2 and even and for p=2,3. And we explore the applications of this labeling in wireless networks.

While many organizations provide a website in multiple languages, few provide a sign-language version for deaf users, many of whom have lower written-language literacy. Rather than providing difficult-to-update videos of humans, a more practical solution would be for the organization to specify a script (representing the sequence of words) to generate a sign-language animation. The challenge is we must select the accurate speed and timing of signs. In this work, focused on American Sign Language (ASL), motion-capture data recorded from humans is used to train machine learning models to calculate realistic timing for ASL animation movement, with an initial focus on inserting prosodic breaks (pauses), adjusting the pause durations for these pauses, and adjusting differentials signing rate for ASL animations based on the sentence syntax and other features. The methodology includes processing and cleaning data from an ASL corpus with motion-capture recordings, selecting features, and building machine learning models to predict where to insert pauses, length of pauses, and signing speed. The resulting models were evaluated using a cross-validation approach to train and test multiple models on various partitions of the dataset, to compare various learning algorithms and subsets of features. In addition, a user-based evaluation was conducted in which native ASL signers evaluated animations generated based on these models. This paper summarizes the motivations for this work, proposed solution, and the potential contribution of this work. This paper describes both completed work and some additional future research plans.

An analysis of machine learning models for sentiment analysis of Tamil code-mixed data

The fastest deterministic algorithms for connected components take logarithmic time and perform superlinear work on a Parallel Random Access Machine (PRAM). These algorithms maintain a spanning forest by merging and compressing trees, which requires pointer-chasing operations that increase memory access latency and are limited to shared-memory systems. Many of these PRAM algorithms are also very complicated to implement. Another popular method is “leader-contraction” where the challenge is to select a constant fraction of leaders that are adjacent to a constant fraction of non-leaders with high probability, but this can require adding more edges than were in the original graph. Instead we investigate label propagation because it is deterministic, easy to implement, and does not rely on pointer-chasing. Label propagation exchanges representative labels within a component using simple graph traversal, but it is inherently difficult to complete in a sublinear number of steps. We are able to overcome the problems with label propagation for graph connectivity. We introduce a surprisingly simple framework for deterministic, undirected graph connectivity using label propagation that is easily adaptable to many computational models. It achieves logarithmic convergence independently of the number of processors and without increasing the edge count. We employ a novel method of propagating directed edges in alternating direction while performing minimum reduction on vertex labels. We present new algorithms in PRAM, Stream, and MapReduce. Given a simple, undirected graph [Formula: see text] with [Formula: see text] vertices, [Formula: see text] edges, our approach takes O(m) work each step, but we can only prove logarithmic convergence on a path graph. It was conjectured by Liu and Tarjan (2019) to take [Formula: see text] steps or possibly [Formula: see text] steps. Our experiments on a range of difficult graphs also suggest logarithmic convergence. We leave the proof of convergence as an open problem.