Forcing matching numbers of fullerene graphs

Zhang, Heping; Ye, Dong; Shiu, Wai Chee

doi:10.1016/j.dam.2009.10.013

Cited by 39 publications

(25 citation statements)

References 24 publications

(25 reference statements)

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“…9 Zhang, Ye, and Shiu have found lower bounds for the forcing number (of a maximum matching) of fullerenes. 10 Vukičević and Trinajstić have investigated the anti-forcing number of benzenoids, the smallest number of edges that must be removed from a benzenoid so that a single Kekulé structure remains. …”

Section: They Showmentioning

confidence: 99%

Forcing Independence

Larson¹,

Cleemput²

2013

Croat. Chem. Acta

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Abstract. An independent set in a graph is a set of vertices which are pairwise non-adjacent. An independent set of vertices F is a forcing independent set if there is a unique maximum independent set I such that F ⊆ I. The forcing independence number or forcing number of a maximum independent set I is the cardinality of a minimum forcing set for I. The forcing number f of a graph is the minimum cardinality of the forcing numbers for the maximum independent sets of the graph. The possible values of f are determined and characterized. We investigate connections between these concepts, other structural concepts, and chemical applications. (doi: 10.5562/cca2295)

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Section: They Showmentioning

confidence: 99%

Forcing Independence

Larson¹,

Cleemput²

2013

Croat. Chem. Acta

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“…And further, what has been termed an "anti-forcing" idea has also been proposed 17 & studied. 17,[28][29][30][31][32][33] All this would surely immensely please Frank -including the evident efficacy of his nomenclature, such as deeply interested him, in a very general context. Now perhaps is a good time to emphasize the wider generality of the "forcing" idea, as is attempted here, indicating that "anti-forcing" is part of this broad general picture, with further illustration of the extended idea, though first retaining the context of Kekule struc-tures.…”

Section: Hystory and Motivationmentioning

confidence: 99%

“…[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] But it should be mentioned that not all Kekule structures of general graphs admit a 6-forcing set, and consequently do not admit a 6-freedom. Such clearly is the circumstance with any multi-Kekulean graph without any 6-cycles -e.g., the 4-cycle (butadiene).…”

Section: Admissability Of 6-forcing and E6-forcingmentioning

confidence: 99%

“…He encouraged collaboration on the topic, which indeed ensued: a degree of concurrence of opinions was achieved, some initial results were established (on forcing, and some other ideas), and a paper subsequently appeared. 6 Following this work, forcing for Kekule structures has continued to receive attention, in both the mathematical, [7][8][9][10][11][12][13][14][15][16][17][18] and the chemical [19][20][21][22][23][24][25][26][27] literature. And further, what has been termed an "anti-forcing" idea has also been proposed 17 & studied.…”

Section: Hystory and Motivationmentioning

confidence: 99%

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Forcing, Freedom, & Uniqueness in Graph Theory & Chemistry

Klein

Rosenfeld

2014

Croat. Chem. Acta

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Abstract. Harary's & Randić's ideas of "forcing" & "freedom" involve subsets of double bonds of Kekule structure such as to be unique to that Kekule structure. Such forcing sets are argued to be greatly generalizable to deal with various other coverings, and thence forcing seems to be fundamental, and of notable potential utility. Various forcing invariants associated to (molecular) graphs ensue, with illustrative (chemical) examples and some mathematical consequences being provided. A complementary "uniqueness" idea is noted, and the general characteristic of "derivativity" of "forcing" is established (as is relevant for QSPR fittings). Different ways in which different sorts of forcings arise in chemistry are briefly indicated.(doi: 10.5562/cca2000)

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“…And then the forcing concept is applied in various graph parameters viz. geodetic sets, hull sets, matching's, Steiner sets and edge covering in [3,4,6,8,10 ] by several authors. In this paper we study the forcing concept in minimum edge-to-vertex geodetic set of a connected graph.…”

Section: Introductionmentioning

confidence: 99%

The Forcing Edge-to-Vertex Geodetic Number of a Graph

Sujitha¹,

John²,

Vijayan³

2015

Int. J. of Pure and Appl. Math.

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For a connected graph G = (V, E), a set S ⊆ E is called an edge-to-vertex geodetic set of G if every vertex of G is either incident with an edge of S or lies on a geodesic joining a pair of edges of S. The minimum cardinality of an edge-to-vertex geodetic set of G is g ev (G). Any edge-to-vertex geodetic set of cardinality g ev (G) is called an edge-to-vertex geodetic basis of G. A subset T ⊆ S is called a forcing subset for S if S is the unique minimum edge-to-vertex geodetic set containing T . A forcing subset for S of minimum cardinality is a minimum forcing subset of S. The forcing edge-to-vertex geodetic number of S, denoted by f ev (S), is the cardinality of a minimum forcing subset of S. The forcing edge-to-vertex geodetic number of G, denoted by f ev (G), is f ev (G) = min {f ev (S)}, where the minimum is taken over all minimum edgeto-vertex geodetic sets S in G. Some general properties satisfied by the concept forcing edge-to-vertex geodetic number is studied. The forcing edge-to-vertex geodetic number of certain classes of graphs are determined. It is shown that

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Forcing matching numbers of fullerene graphs

Cited by 39 publications

References 24 publications

Forcing Independence

Forcing Independence

Forcing, Freedom, & Uniqueness in Graph Theory & Chemistry

The Forcing Edge-to-Vertex Geodetic Number of a Graph

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