• Title/Summary/Keyword: Graph

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ON PAIR MEAN CORDIAL GRAPHS

  • R. PONRAJ;S. PRABHU
    • Journal of Applied and Pure Mathematics
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    • v.5 no.3_4
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    • pp.237-253
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    • 2023
  • Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}=\{\array{{\frac{p}{2}} & \;\;p\text{ is even} \\ {\frac{p-1}{2}} & \;\;p\text{ is odd,}$$ and M = {±1, ±2, … ± ρ} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling ${\frac{{\lambda}(u)+{\lambda}(v)}{2}}$ if λ(u) + λ(v) is even and ${\frac{{\lambda}(u)+{\lambda}(v)+1}{2}}$ if λ(u) + λ(v) is odd such that ${\mid}{\bar{{\mathbb{S}}}}_{\lambda}{_1}-{\bar{{\mathbb{S}}}}_{{\lambda}^c_1}{\mid}{\leq}1$ where ${\bar{{\mathbb{S}}}}_{\lambda}{_1}$ and ${\bar{{\mathbb{S}}}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G for which there exists a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling behavior of few graphs including the closed helm graph, web graph, jewel graph, sunflower graph, flower graph, tadpole graph, dumbbell graph, umbrella graph, butterfly graph, jelly fish, triangular book graph, quadrilateral book graph.

Embedding between a Macro-Star Graph and a Matrix Star Graph (매크로-스타 그래프와 행렬 스타 그래프 사이의 임베딩)

  • Lee, Hyeong-Ok
    • The Transactions of the Korea Information Processing Society
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    • v.6 no.3
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    • pp.571-579
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    • 1999
  • A Macro-Star graph which has a star graph as a basic module has node symmetry, maximum fault tolerance, and hierarchical decomposition property. And, it is an interconnection network which improves a network cost against a star graph. A matrix star graph also has such good properties of a Macro-Star graph and is an interconnection network which has a lower network cost than a Maco-Star graph. In this paper, we propose a method to embed between a Macro-Star graph and a matrix star graph. We show that a Macro-Star graph MS(k, n) can be embedded into a matrix star graph MS\ulcorner with dilation 2. In addition, we show that a matrix star graph MS\ulcorner can be embedded into a Macro-Star graph MS(k,n+1) with dilation 4 and average dilation 3 or less as well. This result means that several algorithms developed in a star graph can be simulated in a matrix star graph with constant cost.

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Fuzzy ideal graphs of a semigroup

  • Rao, Marapureddy Murali Krishna
    • Annals of Fuzzy Mathematics and Informatics
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    • v.16 no.3
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    • pp.363-371
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    • 2018
  • The main objective of this paper is to connect fuzzy theory, graph theory and fuzzy graph theory with algebraic structure. We introduce the notion of fuzzy graph of semigroup, the notion of fuzzy ideal graph of semigroup as a generalization of fuzzy ideal of semigroup, intuitionistic fuzzy ideal of semigroup, fuzzy graph and graph, the notion of isomorphism of fuzzy graphs of semigroups and regular fuzzy graph of semigroup and we study some of their properties.

A Graph Embedding Technique for Weighted Graphs Based on LSTM Autoencoders

  • Seo, Minji;Lee, Ki Yong
    • Journal of Information Processing Systems
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    • v.16 no.6
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    • pp.1407-1423
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    • 2020
  • A graph is a data structure consisting of nodes and edges between these nodes. Graph embedding is to generate a low dimensional vector for a given graph that best represents the characteristics of the graph. Recently, there have been studies on graph embedding, especially using deep learning techniques. However, until now, most deep learning-based graph embedding techniques have focused on unweighted graphs. Therefore, in this paper, we propose a graph embedding technique for weighted graphs based on long short-term memory (LSTM) autoencoders. Given weighted graphs, we traverse each graph to extract node-weight sequences from the graph. Each node-weight sequence represents a path in the graph consisting of nodes and the weights between these nodes. We then train an LSTM autoencoder on the extracted node-weight sequences and encode each nodeweight sequence into a fixed-length vector using the trained LSTM autoencoder. Finally, for each graph, we collect the encoding vectors obtained from the graph and combine them to generate the final embedding vector for the graph. These embedding vectors can be used to classify weighted graphs or to search for similar weighted graphs. The experiments on synthetic and real datasets show that the proposed method is effective in measuring the similarity between weighted graphs.

GraphSLAM Improved by Removing Measurement Outliers (측정 아웃라이어 제거를 통해 개선된 GraphSLAM)

  • Kim, Ryun-Seok;Choi, Hyuk-Doo;Kim, Eun-Tai
    • Journal of the Korean Institute of Intelligent Systems
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    • v.21 no.4
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    • pp.493-498
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    • 2011
  • This paper presents the GraphSLAM improved by selecting the measurement with respect to their likelihoods. GraphSLAM estimates the robot's path and map by utilizing the entire history of input data. However, GraphSLAM's performance suffers a lot from severely noisy measurements. In this paper, we present GraphSLAM improved by the selective measurement method. Thus the presented GraphSLAM provides higher performance compared with the standard GraphSLAM.

Embedding algorithm among star graph and pancake graph, bubblesort graph (스타 그래프와 팬케익, 버블정렬 그래프 사이의 임베딩 알고리즘)

  • Kim, Jong-Seok;Lee, Hyeong-Ok;Kim, Sung-Won
    • The Journal of Korean Association of Computer Education
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    • v.13 no.5
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    • pp.91-102
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    • 2010
  • Star graph is a well-known interconnection network to further improve the network cost of Hypercube and has good properties such as node symmetry, maximal fault tolerance and strongly hierarchical property. In this study, we will suggest embedding scheme among star graph and pancake graph, bubblesort graph, which are variations of star graph. We will show that bubblesort graph can be embedded into pancake and star graph with dilation 3, expansion 1, respectively and pancake graph can be embedded into bubblesort graph with dilation cost O($n^2$). Additionally, we will show that star graph can be embedded into pancake graph with dilation 4, expansion 1. Also, with dilation cost O(n) we will prove that star graph can be embedded into bubblesort graph and pancake graph can be embedded into star graph.

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The Status Quo of Graph Databases in Construction Research

  • Jeon, Kahyun;Lee, Ghang
    • International conference on construction engineering and project management
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    • 2022.06a
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    • pp.800-807
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    • 2022
  • This study aims to review the use of graph databases in construction research. Based on the diagnosis of the current research status, a future research direction is proposed. The use of graph databases in construction research has been increasing because of the efficiency in expressing complex relations between entities in construction big data. However, no study has been conducted to review systematically the status quo of graph databases. This study analyzes 42 papers in total that deployed a graph model and graph database in construction research, both quantitatively and qualitatively. A keyword analysis, topic modeling, and qualitative content analysis were conducted. The review identified the research topics, types of data sources that compose a graph, and the graph database application methods and algorithms. Although the current research is still in a nascent stage, the graph database research has great potential to develop into an advanced stage, fused with artificial intelligence (AI) in the future, based on the active usage trends this study revealed.

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AUGMENTED INVERSE GRAPHS WITH RESPECT TO A GROUP

  • M. LAKSHMI KAMESWARI;N. NAGA MARUTHI KUMARI;T.V. PRADEEP KUMAR
    • Journal of applied mathematics & informatics
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    • v.41 no.2
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    • pp.287-293
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    • 2023
  • In this paper, the Augmented graph Es(τ) of the inverse graph Gs(τ) of a cyclic group (τ,◦) was studied. The Augmented inverse graph was constructed by applying the method of Mycielski's construction. The dimension of Augmented inverse graph and different properties of the graph were investigated. Later the chromatic number of Augmented inverse graph was discussed and the relation between the maximum degree of the graph and the chromatic number was established. In the Mycielski's construction, the properties of the key node 'u' in Es (τ) were established based on cardinality of the cyclic group (τ,◦) and also proved that the Augmented inverse graph Es(τ) was a triangle free graph.

ℂ-VALUED FREE PROBABILITY ON A GRAPH VON NEUMANN ALGEBRA

  • Cho, Il-Woo
    • Journal of the Korean Mathematical Society
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    • v.47 no.3
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    • pp.601-631
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    • 2010
  • In [6] and [7], we introduced graph von Neumann algebras which are the (groupoid) crossed product algebras of von Neumann algebras and graph groupoids via groupoid actions. We showed that such crossed product algebras have the graph-depending amalgamated reduced free probabilistic properties. In this paper, we will consider a scalar-valued $W^*$-probability on a given graph von Neumann algebra. We show that a diagonal graph $W^*$-probability space (as a scalar-valued $W^*$-probability space) and a graph W¤-probability space (as an amalgamated $W^*$-probability space) are compatible. By this compatibility, we can find the relation between amalgamated free distributions and scalar-valued free distributions on a graph von Neumann algebra. Under this compatibility, we observe the scalar-valued freeness on a graph von Neumann algebra.