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About 5,505 papers for “Interval graph”

Interval Graph Limits

Persi Diaconis, Susan Holmes, Svante Janson · Annals of Combinatorics · 2012

Cited by 16

Interval graph mining

Yahia Lebbah, Amina Kemmar, Samir Loudni · International Journal of Data Mining Modelling and Management · 2018

Frequent subgraph mining is a difficult data mining problem aiming to find the exact set of frequent subgraphs into a database of graphs. Current subgraph mining approaches make use of the canonical encoding which is one of the key operations. It is well known that canonical encodings have an exponential time complexity. Consequently, mining all frequent patterns for large and dense graphs is computationally expensive. In this paper, we propose an interval approach to handle canonicity, leading to two encodings, lower and upper encodings, with a polynomial time complexity, allowing to tightly enclose the exact set of frequent subgraphs. These two encodings lead to an interval graph mining algorithm where two minings are launched in parallel, a lower mining (resp. upper mining) using the lower (resp. upper) encoding. The interval graph mining approach has been implemented within the state of the art Gaston miner. Experiments performed on synthetic and real graph databases coming from stock market and biological datasets show that our interval graph mining is effective on dense graphs.

Cited by 0Open access

Interval graph mining

Amina Kemmar, Yahia Lebbah, Samir Loudni · International Journal of Data Mining Modelling and Management · 2018

Frequent subgraph mining is a difficult data mining problem aiming to find the exact set of frequent subgraphs into a database of graphs. Current subgraph mining approaches make use of the canonical encoding which is one of the key operations. It is well known that canonical encodings have an exponential time complexity. Consequently, mining all frequent patterns for large and dense graphs is computationally expensive. In this paper, we propose an interval approach to handle canonicity, leading to two encodings, lower and upper encodings, with a polynomial time complexity, allowing to tightly enclose the exact set of frequent subgraphs. These two encodings lead to an interval graph mining algorithm where two minings are launched in parallel, a lower mining (resp. upper mining) using the lower (resp. upper) encoding. The interval graph mining approach has been implemented within the state of the art Gaston miner. Experiments performed on synthetic and real graph databases coming from stock market and biological datasets show that our interval graph mining is effective on dense graphs.

Cited by 0Open access

Interval graph mining

Kemmar Amina, Yahia Lebbah, Samir Loudni · HAL (Le Centre pour la Communication Scientifique Directe) · 2018

International audience

Cited by 0

INTERVAL VALUED SIGNED NEUTROSOPHIC GRAPH

SUDHAKAR.V.J, MOHAMED ALI. A, VINOTH.D · Zenodo (CERN European Organization for Nuclear Research) · 2019

The notion of interval valued neutrosophic sets is a generalization of fuzzy sets, intuitionistic fuzzy sets, interval valued fuzzy sets, interval valued intuitionstic fuzzy sets and single valued neutrosophicsets. We apply for the first time the concept of interval valued neutrosophic sets, an instance of neutrosophic sets, to the graph theory. We introduce certain types of interval valued signed neutrosophc graphs (IVNG) and investigate some of their properties with proof and example.

Cited by 0Open access

Interval-valued fuzzy threshold graph

Tarasankar Pramanik, Madhumangal Pal, Sukumar Mondal · Pacific Science Review A Natural Science and Engineering · 2016

Interval-valued fuzzy threshold graph is an extension of fuzzy threshold graph. In this paper, interval-valued fuzzy threshold graph, interval-valued fuzzy alternating 4-cycle, and interval-valued fuzzy threshold dimension are defined, and certain properties are studied. It is demonstrated that every interval-valued fuzzy threshold graph can be treated as an interval-valued fuzzy split graph.

Cited by 19Open access

North-Holland Publishing Company THE ASYMPTOTIC PROBABILITY THAT A RANDOM GRAPH IS A UNIT INTERVAL GRAPH, INDIFFERENCE GRAPH, OR PROPER INTERVAL GRAPH

Joel E Cohen, J. E. Cohen · 1981

Let G be a graph on u labelled vertices with E edges, without loops or multiple edges. Let u +a and let E = E(u) be a function of u such that lim E ( v) / v n 3 = c. The limit of the probability that a random graph is a unit interval graph, indifference graph or proper interval graph is exp(-$c". Let G be a graph with a finite set A of v labelled vertices and E unlabelled, undirected edges. For x and y in A, x # y, we write x I y if (x, y) is an edge of G. Loops and multiple edges are excluded. G is a unit interval graph [4, p. 1441 if and only if, for each x in A, there exists an interval J(x) of the real line, closed and of unit length, such that x I y if and only if J(x) n J(y) # g. ( 1) Unit interval graphs have applications in psychology, archeology, political science, economics and other fields [4,5]. A random graph with v labelled vertices and E edges is defined [2] as one in which the E edges are chosen randomly, without replacement, from the (;) possible edges so that all C,., possible graphs are equiprobable, where If U,., is the number of graphs on v labelled vertices and E edges that are unit interval graphs, then the probability P,., (u.i.g.) that a random graph on v labelled vertices and E edges is a unit interval graph is U,,,/C,,,. We shall describe the behavior of P,.,(u.i.g.), letting v +a and E =E(v) increase as a function of v.

Cited by 0

Bar graph of red-green interval.

Liat Gantz (702778), Shlomo Schrader (702779), Ruthie Ruben (702780) et al. · Figshare · 2015

<p>The X axis is subject number and Y axis is the interval between “red” and “green” responses in diopters. Blue is with spherical correction only; red is with spherical and cylindrical correction.</p>

Cited by 0Open access

The Interval Count of a Graph

Rochelle Leibowitz, Susan F. Assmann, G. W. Peck · SIAM Journal on Algebraic and Discrete Methods · 1982

The interval count of an interval graph G is the minimum number of different interval sizes needed to represent the vertices of G, where two vertices are adjacent if and only if their intervals intersect. We show that if G is an interval graph and for some vertex x, $G - \{ x \}$ has interval count one, then G has interval count two or less. We also show how to construct examples of interval graphs where the interval count of G exceeds that of $G - \{ x \}$ by at least two when the latter number is two or more.

Cited by 14

The interval function of a graph

Henry Martyn Mulder · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 1980

Cited by 332Open access