Graphs and degree sequences. I

Tyshkevich, R. I.; Chernyak, A. A.; Chernyak, Zh. A.

doi:10.1007/bf01070234

Cited by 18 publications

(10 citation statements)

References 101 publications

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“…In the case of bipartite sequences, a characterization known as the Gale-Ryser theorem [13,22,24] leads to efficient sequential algorithms for the decision as well as the search problems. Recently, degree sequence problems have gained lot of attention, see for example [2,3,4,9,21,23,25,26].…”

Section: Previous Resultsmentioning

confidence: 99%

Realizing degree sequences in parallel

Arikati

Maheshwari

1994

Algorithms and Computation

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A sequence d of integers is a degree sequence if there exists a (simple) graph G such that the components of d are equal to the degrees of the vertices of G. The graph G is said to be a realization of d. We provide an efficient parallel algorithm to realize d; the algorithm runs in O(log n) time using O(n + m) CRCW PRAM processors, where n and m are the number of vertices and edges in G. Before our result, it was not known if the problem of realizing d is in N C.

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Section: Previous Resultsmentioning

confidence: 99%

Realizing degree sequences in parallel

Arikati

Maheshwari

1994

Algorithms and Computation

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“…al. established a relation between degree sequence of a graph and some structural properties of a graph [14], [15]. Equivalently, given an undirected graph, a degree sequence is a monotonic non-increasing sequence of the vertex degrees (valencies) of its graph vertices.…”

Section: Graph Operators and Degree Sequencementioning

confidence: 99%

Degree Sequence of Graph Operator for some Standard Graphs

Harisha¹,

Ranjini

Lokesha

et al. 2020

Applied Mathematics and Nonlinear Sciences

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Topological indices play a very important role in the mathematical chemistry. The topological indices are numerical parameters of a graph. The degree sequence is obtained by considering the set of vertex degree of a graph. Graph operators are the ones which are used to obtain another broader graphs. This paper attempts to find degree sequence of vertex–F join operation of graphs for some standard graphs.

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“…The same year, Tyshkevich et al established a correspondence between DS of a graph and some structural properties of this graph [5]. In 1987, Tychkevich et al [6] written a survey on the same correspondence . In [7], the authors gave a new version of the Erdös-Gallai theorem on the realizability of a given DS.…”

Section: Narumi-katayama Index Of Double Graphsmentioning

confidence: 99%

Narumi–Katayama index of the subdivision graphs

Aşçıoğlu

Cangül

2018

Journal of Taibah University for Science

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Subdivision is an important aspect in graph theory which allows one to calculate properties of some complicated graphs in terms of some easier graphs. Recently, the notion of r-subdivision was similarly defined as a quite useful generalization by adding r new vertices to each edge. Also the double graphs are used to ease some calculations, especially with the chemical graphs. Topological graph indices have become popular due to their applications in chemistry or related areas due to their advantages over time and money consuming laboratory experiments. In this paper, we calculate one of the topological graph indices, namely the Narumi-Katayama index of the subdivision, r-subdivision, double, subdivision of double and double of subdivision graphs of any given graph. We give some symmetry relations and results for the well-known graph classes.

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Graphs and degree sequences. I

Cited by 18 publications

References 101 publications

Realizing degree sequences in parallel

Realizing degree sequences in parallel

Degree Sequence of Graph Operator for some Standard Graphs

Narumi–Katayama index of the subdivision graphs

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