Geodesic
Generating function for representations of graphs by $k$-partite graphs
Prikladnaâ diskretnaâ matematika, no. 1 (2016), pp. 5-12.

Voir la notice de l'article provenant de la source Math-Net.Ru

A relation between the generating function of $k$-partite graphs and the generating function of the number of $k$-partite representations of graphs is obtained. A correlation between the relation's coefficients and chromatic polynomial coefficients is shown. An application of the results to calculation of weighted sums is demonstrated. Special cases of sums and some applications of the relations in physics and mathematics are considered.
Keywords: graph, hypergraph, multigraph, generating functions, chromatic polynomial, weighted sum.
Mots-clés : $k$-partite graph 
@article{PDM_2016_1_a0,
     author = {R. M. Ganopolsky},
     title = {Generating function for representations of graphs by $k$-partite graphs},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {5--12},
     publisher = {mathdoc},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2016_1_a0/}
}
TY  - JOUR
AU  - R. M. Ganopolsky
TI  - Generating function for representations of graphs by $k$-partite graphs
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2016
SP  - 5
EP  - 12
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2016_1_a0/
LA  - ru
ID  - PDM_2016_1_a0
ER  - 
%0 Journal Article
%A R. M. Ganopolsky
%T Generating function for representations of graphs by $k$-partite graphs
%J Prikladnaâ diskretnaâ matematika
%D 2016
%P 5-12
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2016_1_a0/
%G ru
%F PDM_2016_1_a0
R. M. Ganopolsky. Generating function for representations of graphs by $k$-partite graphs. Prikladnaâ diskretnaâ matematika, no. 1 (2016), pp. 5-12. http://geodesic.mathdoc.fr/item/PDM_2016_1_a0/

[1] Ganopol'skiy R. M., “The exponential generating functions for sequence of the numbers of $k$-partite graphs”, Prikladnaya Diskretnaya Matematika, 2015, no. 1(27), 84–91 (in Russian)

[2] Stenli R., Enumerative Combinatorics. The Trees, Generating Functions and Symmetric Functions, Mir Publ., Moscow, 2005 (in Russian) | MR

[3] Ganopolsky R. M., “The number of disordered covers of a finite set by subsets having fixed cardinalities”, Prikladnaya Diskretnaya Matematika, 2010, no. 4(10), 5–17 (in Russian)

[4] Ganopolsky R. M., “Generating functions for sequences of disordered covers numbers”, Prikladnaya Diskretnaya Matematika, 2011, no. 1(11), 5–13 (in Russian)

[5] Ganopolsky R. M., “Generating functions for sequences of connected covers numbers”, Prikladnaya Diskretnaya Matematika, 2013, no. 3(21), 5–10 (in Russian)

[6] Graham R. L., Knuth D. E., Patashnik O., Concrete Mathematics, Addison-Wesley, Reading, MA, 1994 | MR | Zbl

[7] Harary F., Graph Theory, Addison-Wesley, Reading, MA, 1994 | MR

[8] Kaku M., Introduction to Superstrings, Springer Verlag, 1988 | MR | Zbl

[9] Feynman R., Statistical Mechanics. Lecture Course, Mir Publ., Moscow, 1975 (in Russian)

[10] Abrikosov A. A., Gor'kov L. P., Dzjaloshinskij I. E., Methods of Quantum Field Theory in Statistical Physics, Fizmatgiz Publ., Moscow, 1962 (in Russian) | MR

[11] Lifshic E. M., Pitaevskij L. P., Statistical Physics, Part 2, Nauka Publ., Moscow, 1978 (in Russian) | MR

[12] Fomichev V. M., Methods of Discrete Mathematics in Cryptology, Dialog-MIFI Publ., Moscow, 2010 (in Russian)