Trees with a given number of leaves and the maximal number of maximum independent sets

References

[1] Taletskii D. S., Malyshev D. S., “On trees of bounded degree with maximal number of greatest independent sets”, J. Appl. Industr. Math., 12:2 (2018), 369–381.10.1134/S1990478918020175Search in Google Scholar

[2] Taletskii D. S., Malyshev D. S., “Trees without twin-leaves with smallest number of maximal independent sets”, Discrete Math. Appl., 30:1 (2020), 53–67.10.1515/dma-2020-0006Search in Google Scholar

[3] Aimei Y., Xuezheng L., “The Merrifield–Simmons indices and Hosoya indices of trees with k pendant vertices”, J. Math. Chem., 41:1 (2007), 33–43.10.1007/s10910-006-9088-7Search in Google Scholar

[4] Chen Y.,Wen S., “On the total number of matchings of trees with prescribed diameter”, Int. J. Nonlin. Sci., 4:1 (2007), 37–43.Search in Google Scholar

[5] Dainyak A. B., “On the number of independent sets in the trees of a fixed diameter”, J. Appl. Industr.Math., 4:2 (2010), 163–171.10.1134/S1990478910020043Search in Google Scholar

[6] Griggs J., Grinstead C., Guichard D., “The number of maximal independent sets in a connected graph”, Discr. Math., 68:2–3 (1988), 211–220.10.1016/0012-365X(88)90114-8Search in Google Scholar

[7] Hanyuan D., Qiuzhi G., “On the minimalMerrifield–Simmons index of trees of order n with at least ⌊n2⌋+1 pendant vertices”, MATCH Commun. in Math. and Comput. Chem., 60 (2008), 601–608.Search in Google Scholar

[8] Heuberger C.,Wagner S., “Maximizing the number of independent subsets over trees with bounded degree”, J. Graph Theory, 58:1 (2008), 49–68.10.1002/jgt.20294Search in Google Scholar

[9] Hopkins G., Staton W., “Graphs with unique maximum independent sets”, Discr. Math., 57 (1985), 245–251.10.1016/0012-365X(85)90177-3Search in Google Scholar

[10] Hujter M., Tuza Z., “The number of maximal independent sets in triangle-free graphs”, SIAM J. Discr. Math., 6:2 (1993), 284– 288.10.1137/0406022Search in Google Scholar

[11] Jou M., Chang G., “Maximal independent sets in graphs with at most one cycle”, Discr. Appl. Math., 79:1–3 (1997), 67–73.10.1016/S0166-218X(97)00033-4Search in Google Scholar

[12] Jou M., Chang G., “The number of maximum independent sets in graphs”, J. Graph Theory, 4:4 (2000), 685–695.10.11650/twjm/1500407302Search in Google Scholar

[13] Knopfmacher A., Tichy R. F., Wagner S., Ziegler V., “Graphs, partitions and Fibonacci numbers”, Discr. Appl. Math., 155:10 (2007), 1175–1187.10.1016/j.dam.2006.10.010Search in Google Scholar

[14] Li X., Zhao H., Gutman I., “On the Merrifield–Simmons index of trees”, MATCH Commun. Math. and Comput. Chem., 54:2 (2005), 389–402.Search in Google Scholar

[15] Liu J., “Maximal independent sets in bipartite graphs”, J. Graph Theory, 17:1 (1993), 495–507.10.1002/jgt.3190170407Search in Google Scholar

[16] Moon J., Moser L., “On cliques in graphs”, Isr. J. Math., 3:1 (1965), 23–28.10.1007/BF02760024Search in Google Scholar

[17] Sagan B. E., “A note on independent sets in trees”, SIAM J. Discr. Math., 1 (1988), 105–108.10.1137/0401012Search in Google Scholar

[18] Pan X.-F., Xu J.-M., Yang C., Zhou M.-J., “Some graphs with minimum Hosoya index and maximum Merrifield–Simmons index”, MATCH Commun. Math. and Comput. Chem., 57 (2007), 235–242.Search in Google Scholar

[19] Wilf H., “The number of maximal independent sets in a tree”, SIAM J. Algebr. Discr. Meth., 7:1 (1986), 125–130.10.1137/0607015Search in Google Scholar

[20] Zito J., “The structure and maximum number of maximum independent sets in trees”, J. Graph Theory, 15:2 (1991), 207–221.10.1002/jgt.3190150208Search in Google Scholar