On the transmission of uniform unicyclic hypergraphs
DOI:
https://doi.org/10.55016/x7bprv29Keywords:
uniform hypergraph, unicyclic hypergraph, transmission, extremal hypergraphAbstract
The transmission of a connected hypergraph is defined as the sum of distances between all unordered pairs of distinct vertices. We determine the unique uniform unicyclic hypergraphs of fixed size with minimum and maximum transmissions, respectively.
References
D. Bienstock, E. Gyori, Average distance in graphs with removed elements, J. Graph Theory 12 (1988) 375--390.
F. R. K. Chung, The average distance and the independence number, J. Graph Theory 12 (1988) 229--235.
P. Dankelmann, R. Entringer, Average distance, minimum degree and spanning trees, J. Graph Theory 33 (2000) 1--13.
A. A. Dobrynin, R. Entringer, I. Gutman, Wiener index of trees: theory and applications, Acta Appl. Math. 66 (2001) 211--249.
J. K. Doyle, J. E. Graver, Mean distance in a graph, Discrete Math. 7 (1977) 147--154.
H. Guo, B. Zhou, Properties of Degree Distance and Gutman Index of Uniform Hypergraphs, MATCH Commun. Math. Comput. Chem. 78 (2017) 213--220
H. Guo, B. Zhou, H. Lin, The Wiener index of uniform hypergraphs, MATCH Commun. Math. Comput. Chem. 78 (2017) 133--152.
I. Gutman, E. V. Konstantinova, V. A. Skorobogatov,
Molecular hypergraphs and Clar structural formulas of benzenoid hydrocarbons, ACH--Models Chem. 136 (1999) 539--548.
P. J. Hansen, J. P. Jurs, Chemical applications of graph theory. Part I. Fundamentals and topological indices, J. Chem. Educ. 65 (1988) 574--580.
G.R.T. Hendry, On mean distance in certain classes of graphs, Networks 19(1989) 451--457.
H. Hosoya, Topological index. A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons, Bull. Chem. Soc. Japan 44 (1971) 2332--2339.
E. V. Konstantinova, V. A. Skoroboratov, Graph and hypergraph models of molecular structure: A comparative analysis of indices, J. Struct. Chem. 39 (1998) 958--966.
E. V. Konstantinova, V. A. Skorobogatov, Application of hypergraph theory in chemistry, Discrete Math. 235 (2001) 365--383.
E. V. Konstantinova, Chemical Hypergraph Theory , Com$^2$MaC Lecture Note Series, Vol. 3, Combinatorial and Computational Mathematics Center, Pohang University of Science and Technology, 2001.
M. Kouider, P. Winkler, Mean distance and minimum degree, J. Graph Theory 25 (1997) 95--99.
B. Mohar, Eigenvalues, diameter and mean distance in graphs, Graphs Combin. 7 (1991) 53--64.
S. Nikoli\'c, N. Trinajsti\'c, Z. Mihali\'c, The Wiener index: Development and applications, Croat. Chem. Acta 68 (1995) 105--128.
J. Plesn\'ik, On the sum of all distances in a graph or digraph, J. Graph Theory 8 (1984) 1--21.
D. H. Rouvray, Predicting chemistry from topology, Sci. Amer. 255 (1986) 40--47.
D. H. Rouvray, The rich legacy of half a century of the Wiener index, in: D.H. Rouvray and R.B. King (Eds.), Topology in Chemistry: Discrete Mathematics of Molecules, Horwood, Chichester, 2002, pp. 16--37.
L. Sun, J. Wu, H. Cai, Z. Luo, The Wiener index of $r$-uniform hypergraph, Bull. Malays. Math. Sci. Soc., in press, DOI: 10.1007/s40840-016-0359-6.
Z. Tang, H. Deng, The $(n,n)$-graphs with the first three extremal Wiener indices, J. Math. Chem. 43 (2008) 60--74.
H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947) 17--20.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Contributions to Discrete Mathematics
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
This copyright statement was adapted from the statement for the University of Calgary Repository and from the statement for the Electronic Journal of Combinatorics (with permission).
The copyright policy for Contributions to Discrete Mathematics (CDM) is changed for all articles appearing in issues of the journal starting from Volume 15 Number 3.
Author(s) retain copyright over submissions published starting from Volume 15 number 3. When the author(s) indicate approval of the finalized version of the article provided by the technical editors of the journal and indicate approval, they grant to Contributions to Discrete Mathematics (CDM) a world-wide, irrevocable, royalty free, non-exclusive license as described below:
The author(s) grant to CDM the right to reproduce, translate (as defined below), and/or distribute the material, including the abstract, in print and electronic format, including but not limited to audio or video.
The author(s) agree that the journal may translate, without changing the content the material, to any medium or format for the purposes of preservation.
The author(s) also agree that the journal may keep more than one copy of the article for the purposes of security, back-up, and preservation.
In granting the journal this license the author(s) warrant that the work is their original work and that they have the right to grant the rights contained in this license.
The authors represent that the work does not, to the best of their knowledge, infringe upon anyone’s copyright.
If the work contains material for which the author(s) do not hold copyright, the author(s) represent that the unrestricted permission of the copyright holder(s) to grant CDM the rights required by this license has been obtained, and that such third-party owned material is clearly identified and acknowledged within the text or content of the work.
The author(s) agree to ensure, to the extent reasonably possible, that further publication of the Work, with the same or substantially the same content, will acknowledge prior publication in CDM.
The journal highly recommends that the work be published with a Creative Commons license. Unless otherwise arranged at the time the finalized version is approved and the licence granted with CDM, the work will appear with the CC-BY-ND logo. Here is the site to get more detail, and an excerpt from the site about the CC-BY-ND. https://creativecommons.org/licenses/
Attribution-NoDerivs
CC BY-ND
This license lets others reuse the work for any purpose, including commercially; however, it cannot be shared with others in adapted form, and credit must be provided to you.