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About 9,894 papers for “Regular graph”

Plithogenic Line Graph, Star Graph, and Regular Graph

Takao Fujita · Plithogenic Logic and Computation · 2025

Graph theory, a branch of mathematics, studies relationships between entities using vertices and edges. In this field, Uncertain Graph Theory has emerged to capture the uncertainties inherent in real-world networks. While Turiyam Neutrosophic and Plithogenic Graphs are established within uncertain graph theory, concepts such as Line Graphs, Star Graphs, and Regular Graphs have not been extensively explored in these frameworks. This paper seeks to fill this gap by introducing and developing the concepts of Line Graph, Star Graph, and Regular Graph specifically within the contexts of Turiyam Neutrosophic and Plithogenic Graphs.

Cited by 0Open access

Regular Rooted Graph Grammars

Sacha Berger · Electronic Theses of LMU Munich (Ludwig-Maximilians-Universität München) · 2008

In dieser Arbeit wir ein pragmatischer Ansatz zur Typisierung, statischen Analyse und Optimierung von Web-Anfragespachen, speziell Xcerpt, untersucht. Pragmatisch ist der Ansatz in dem Sinne, dass dem Benutzer keinerlei Einschränkungen aus Entscheidbarkeits- oder Effizienzgründen auf modellierbare Typen gestellt werden. Effizienz und Entscheidbarkeit werden stattdessen, falls nötig, durch Vergröberungen bei der Typprüfung erkauft. Eine Typsprache zur Typisierung von Graph-strukturierten Daten im Web wird eingeführt. Modellierbare Graphen sind so genannte gewurzelte Graphen, welche aus einem Spannbaum und Querreferenzen aufgebaut sind. Die Typsprache basiert auf reguläre Baum Grammatiken, welche um typisierte Referenzen erweitert wurde. Neben wie im Web mit XML üblichen geordneten strukturierten Daten, sind auch ungeordnete Daten, wie etwa in Xcerpt oder RDF üblich, modellierbar. Der dazu verwendete Ansatz---ungeordnete Interpretation Regulärer Ausdrücke---ist neu. Eine operationale Semantik für geordnete wie ungeordnete Typen wird auf Basis spezialisierter Baumautomaten und sog. Counting Constraints (welche wiederum auf presburgerarithmetische Ausdrücke) basieren. Es wird ferner statische Typ-Prüfung und -Inferenz von Xcerpt Anfrage- und Konstrukttermen, wie auch Optimierung von Xcerpt Anfragen auf Basis von Typinformation eingeführt.

Cited by 0Open access

Numerous graph energies of regular subdivision graph and complete graph

Imrana Kousar, Saima Nazeer, Abid Mahboob et al. · Greater South Information System · 2021

The graph energy $ E(G) $ of a simple graph $ G $ is sum of its absolute eigenvalues where eigenvalues of adjacency matrix $ A(G) $ are referred as eigenvalues of graph $ G $. Depends upon eigenvalues of different graph matrices, several graph energies has been observed recently such as maximum degree energy, Randi$ \acute{c} $ energy, sum-connectivity energy etc. Depending on the definition of a graph matrix, the graph energy can be easily determined. This article contains upper bounds of several graph energies of $ s $-regular subdivision graph $ S(G) $. Also various graph energies of complete graph are mentioned in this article.

Cited by 0Open access

Numerous graph energies of regular subdivision graph and complete graph

Imrana Kousar, Saima Nazeer, Abid Mahboob et al. · AIMS Mathematics · 2021

<abstract> The graph energy $ E(G) $ of a simple graph $ G $ is sum of its absolute eigenvalues where eigenvalues of adjacency matrix $ A(G) $ are referred as eigenvalues of graph $ G $. Depends upon eigenvalues of different graph matrices, several graph energies has been observed recently such as maximum degree energy, Randi$ \acute{c} $ energy, sum-connectivity energy etc. Depending on the definition of a graph matrix, the graph energy can be easily determined. This article contains upper bounds of several graph energies of $ s $-regular subdivision graph $ S(G) $. Also various graph energies of complete graph are mentioned in this article. </abstract>

Cited by 3Open access

Minimal 3-regular Penny Graph

Alexander Karabegov, Tanya Khovanova · arXiv (Cornell University) · 2026

We prove that a 3-regular penny graph has at least 16 vertices and show that such a graph with 16 vertices exists.

Cited by 0Open access

A Questionable Distance-Regular Graph

Rebecca Ross · 2016

Abstract In this paper, we introduce distance-regular graphs and develop the intersection algebra for these graphs which is based upon its intersection numbers. We discuss results following from the definition of the intersection algebra. We investigate two examples of distance-regular graphs and show how these results apply. Finally, we introduce parameters that determine intersection numbers. We investigate if these intersection numbers are nonnegative and feasible. 1.

Cited by 0

On regular spherical fuzzy graph

B. Mohamed Harif, NAZEERA BEGAM · SHILAP Revista de lepidopterología · 2023

A spherical fuzzy set is an advanced extension of clas-sical fuzzy set in which it has an added advantage to deal with awider sense of applicability in uncertain situations. In this paper,regular spherical fuzzy graphs and totally regular spherical fuzzy graphs are introduced. A necessary and sufficient condition for reg-ular spherical fuzzy graphs is given.Some properties of regular and totally regular spherical fuzzy graphs are studied.

Cited by 0Open access

Circumference of a regular graph

Min Aung · Journal of Graph Theory · 1989

Abstract It is proved that a 4‐connected, δ‐regular graph G either is Hamiltonian, or has at least 3δ + 1 vertices and contains a cycle of length at least min{4δ ‐ 4, 1/2 (|G| + 3δ ‐ 2)}. Examples supplied by B. Jackson and H.A. Jung show that min{4δ ‐ 4, 1/2(|G| + 3δ ‐ 2)} cannot be replaced by 4δ + 1.

Cited by 6

Regular embeddings of a graph

Hiroshi Maehara · Pacific Journal of Mathematics · 1983

In this paper we study embeddings of a graph G in Euclidean space R" that are 'regular' in the following sense: given any two distinct vertices u and v of G, the distance between the corresponding points in R" equals a if u and v are adjacent, and equals otherwise. It is shown that for any given value of s -( 2 -a 2 )/ 2 9 the minimum dimension of a Euclidean space in which G is regularly embeddable is determined by the characteristic polynomials of G and (7.

Cited by 24Open access

Regular number of a graph

V. R. Kulli, A. Janakiram, Radha R. Iyer · Journal of Discrete Mathematical Sciences and Cryptography · 2001

Abstract The regular number r(G) of a graph G is the minimum number of subsets into which the edge set of G should be partitioned so that the subgraph induced by each subset is regular. In this chapter some results regarding the regular number r(G) of a graph are established. Also a new parameter edge set independence number of a graph G is defined.

Cited by 5

Regular Queries on Graph Databases

Juan L. Reutter, Miguel Romero, Moshe Y. Vardi · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2015

Graph databases are currently one of the most popular paradigms for storing data. One of the key conceptual differences between graph and relational databases is the focus on navigational queries that ask whether some nodes are connected by paths satisfying certain restrictions. This focus has driven the definition of several different query languages and the subsequent study of their fundamental properties. We define the graph query language of Regular Queries, which is a natural extension of unions of conjunctive 2-way regular path queries (UC2RPQs) and unions of conjunctive nested 2-way regular path queries (UCN2RPQs). Regular queries allow expressing complex regular patterns between nodes. We formalize regular queries as nonrecursive Datalog programs with transitive closure rules. This language has been previously considered, but its algorithmic properties are not well understood. Our main contribution is to show elementary tight bounds for the containment problem for regular queries. Specifically, we show that this problem is 2EXPSPACE-complete. For all extensions of regular queries known to date, the containment problem turns out to be non-elementary. Together with the fact that evaluating regular queries is not harder than evaluating UCN2RPQs, our results show that regular queries achieve a good balance between expressiveness and complexity, and constitute a well-behaved class that deserves further investigation.

Cited by 27Open access

Construction of semi regular graph

H, AfrinRihana, H, AfrinRihana · Zenodo (CERN European Organization for Nuclear Research) · 2025

Graph theory is widely used to prove many mathematical theorems and models. This paper presents the various techniques of semi-regular graphs to solve problems in different fields of technology in addition to mathematics. We describe different classes of semi-regular graphs and their properties. Further, the paper includes the construction of such graphs and concepts like distance symmetry, k₂ + n, and kₙ + 1. Applications and structural illustrations are discussed in detail.

Cited by 0Open access