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Tricyclic graphs with maximum Merrifield–Simmons index

2010
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Discrete Applied Mathematics
*

., ordered the unicyclic

doi:10.1016/j.dam.2009.09.001
fatcat:zrglxwy3vvfwjpwkvnvckac72u
*graphs**with*given girth according to the*Merrifield*-*Simmons**index*in [24] . ... In [17] , Li et al. characterized the tree*with*the maximal*Merrifield*-*Simmons**index*among the trees*with*given diameter. ...##
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Contents

2010
*
Discrete Applied Mathematics
*

Tan

doi:10.1016/s0166-218x(09)00463-6
fatcat:hfdwh36urzabrjwlzeueqbvwsa
*Tricyclic**graphs**with**maximum**Merrifield*-*Simmons**index*204 Notes M. Atapour, S.M. Sheikholeslami, A.N. Ghameshlou and L. Volkmann Signed star domatic number of a*graph*213 A. Behtoei, M. ... Taeri A characterization of block*graphs*219 M. Fliedner, N. Boysen and A. Scholl Solving symmetric mixed-model multi-level just-in-time scheduling problems 222 H. ...##
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The Hosoya index and the Merrifield–Simmons index

2018
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Journal of Mathematical Chemistry
*

In this article, we give sharp bounds on the Hosoya

doi:10.1007/s10910-018-0937-y
fatcat:2zbuo7vqu5b6bmp2356usch6vi
*index*and the*Merrifield*-*Simmons**index*for connected*graphs*of fixed size. ... As a consequence, we determine all connected*graphs*of any fixed order and size which maximize the*Merrifield*-*Simmons**index*. ... to the*graph**with**maximum**Merrifield*-*Simmons**index*. ...##
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The number of independent sets in a connected graph and its complement

2018
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The Art of Discrete and Applied Mathematics
*

Next, we obtain the minimum and

doi:10.26493/2590-9770.1258.c2b
fatcat:byqtsmw4rbc3la63vgbllko4bi
*maximum*value of i(G)+i(G), where*graph*G is a tree T*with*connected complement and a unicyclic*graph*G*with*connected complement, respectively. ... In each case, we characterize the extremal*graphs*. Finally, we establish an upper bound on the i(G) in terms of the Wiener polarity*index*. ... Then we obtain i(G) + i(G) ≥ 2n + 2D(G) + 2D(G) − 4*with*equality if and only if G ∼ = P 4 . Also, we conjecture that the extremal*graph*which reaches the*maximum*value of i(G) + i(G) is S 2,n−2 . ...##
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Extremal Graph Theory for Degree Sequences
[article]

2015
*
arXiv
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pre-print

eigenvalue, the Wiener

arXiv:1510.01903v1
fatcat:j7dpgr62djf3vl377nppnbn3na
*index*, the Harary*index*, the number of subtrees and the chromatic number etc, in given sets*with*the same tree, unicyclic, graphic degree sequences. ... In particular, we study and characterize the extremal*graphs*having the*maximum*(or minimum) values of*graph*invariants such as (Laplacian, p-Laplacian, signless Laplacian) spectral radius, the first Dirichlet ... Andriantiana [1] proved that the greedy tree has minimum energy, Hosoya*index*and*maximum**Merrifield*-*Simmons**index*. Theorem 4.11 [1] Let π be a tree degree sequence. ...##
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On the number of independent sets in cycle-separated tricyclic graphs

2011
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Computers and Mathematics with Applications
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A cycle-separated

doi:10.1016/j.camwa.2011.01.021
fatcat:sgfdj7pmmbdr3gb3sodtg55zly
*tricyclic**graph*(CSTC*graph*) is a connected simple*graph**with*n vertices and n + 2 edges whose subgraph induced by its cycles consists of three disjoint cycles. ... We show that the tight upper bound for the number of independent sets in the n-vertex CSTC*graphs*is 48 × 2 n−9 + 9 (for n ≥ 9); we also characterize the extremal*graph**with*respect to the aforementioned ... We denote the number of independent sets in a*graph*G by i(G). This is called the Fibonacci number or*Merrifield*-*Simmons**index*of G, too. ...##
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Trees with Given Stability Number and Minimum Number of Stable Sets

2011
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Graphs and Combinatorics
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The invariant F (G) is also known as the

doi:10.1007/s00373-011-1041-2
fatcat:g3z4dlmakfdghcllkeubeuu4ei
*Merrifield*-*Simmons**index*or σ-*index*of the*graph*G [14] . ... Other classes of*graphs*have been considered as well; this includes unicyclic*graphs*[10, 15, 16, 19] , bicyclic*graphs*[3] ,*tricyclic**graphs*[22] , quasi-trees [9] , maximal outerplanar*graphs*[ ...##
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The tight upper bound for the number of matchings of tricyclic graphs

2012
unpublished

We also characterize the n-vertex simple connected

fatcat:2hbhucwbx5cbphz73xcgzuoa5q
*tricyclic**graph*for which the bound is best possible. ... In this paper, we determine the tight upper bound for the number of matchings of connected n-vertex*tricyclic**graphs*. ...*tricyclic**graph**with*the largest z-*index*. ...