Journal ArticleDOI
Cubic graphs with 62 vertices having the same path layer matrix
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TLDR
A new upper bound of 36 vertices for the least order of such cubic graphs is established and is realized by cubic graphs without cut-vertices.Abstract:
The path layer matrix (or path degree sequence) of a graph G contains quantitative information about all possible paths in G. The entry (i,j) of this matrix is the number of paths in G having initial vertex i and length j. It is known that there are cubic graphs on 62 vertices having the same path layer matrix (A. A. Dobrynin. J Graph Theory 17 (1993) 1–4). A new upper bound of 36 vertices for the least order of such cubic graphs is established. This bound is realized by cubic graphs without cut-vertices. © 2001 John Wiley & Sons, Inc. J Graph Theory 38: 177–182, 2001read more
Citations
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Figures of Graph Partitioning by Counting, Sequence and Layer Matrices
TL;DR: The two isomers of C28 fullerenes were colored to test the ability of classifiers to generate different partitions and colorings, thereby providing a useful visual tool for scientists working on the functionalization of various highly symmetrical chemical structures.
Graph Theory. 1. Fragmentation of Structural Graphs
TL;DR: The main subject of the paper is to express fragmentation criteria in graph using a new method of investigation: terminal paths.
Graph Theory. 2. Vertex Descriptors and Graph Coloring
TL;DR: The construction of a set of ten sequence matrices and their applications for ordering vertices in graphs is presented and it is demonstrated that every criterion induced its own partition of graph vertex.
Journal IssueDOI
Small regular graphs having the same path layer matrix
TL;DR: For r-regular graphs with the same path layer matrix, Wang et al. as discussed by the authors gave an upper bound of 4, 5, 6 on the number of simple paths in G having initial vertex i and length j.
Journal ArticleDOI
4-regular graphs without cut-vertices having the same path layer matrix
TL;DR: Dobrynin et al. as discussed by the authors constructed a pair of 4-regular graphs without cut-vertices on 18 vertices having the same path layer matrix, improving the upper bound for the least order of 4regular graphs with the same matrix from 44 to 18.
References
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Journal ArticleDOI
Counterexamples to randić's conjecture on distance degree sequences for trees
TL;DR: As counterexamples to a conjecture of Randic, pairs of nonisomorphic trees with the same collections of distance degree sequences are presented.
Journal ArticleDOI
Graph-based fragment searches in polycyclic structures
Milan Randić,Charles L. Wilkins +1 more
TL;DR: It is shown it is useful to list all paths for all atoms in a structure and then to use such a list for substructure searches, and to comparison of the lists of paths for two graphs permits establishing compatibilities among the vertices.
Journal ArticleDOI
Regular graphs having the same path layer matrix
TL;DR: The path layer matrix (or path degree sequence) of a graph G contains quantitative information about all paths in G, where Elements (i, j) in this matrix is the number of simple paths inG having initial vertex v i and length j.
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