Forcing, Freedom, & Uniqueness in Graph Theory & Chemistry
نویسندگان
چکیده
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)
منابع مشابه
Complete forcing numbers of polyphenyl systems
The idea of “forcing” has long been used in many research fields, such as colorings, orientations, geodetics and dominating sets in graph theory, as well as Latin squares, block designs and Steiner systems in combinatorics (see [1] and the references therein). Recently, the forcing on perfect matchings has been attracting more researchers attention. A forcing set of M is a subset of M contained...
متن کاملAnti-forcing number of some specific graphs
Let $G=(V,E)$ be a simple connected graph. A perfect matching (or Kekul'e structure in chemical literature) of $G$ is a set of disjoint edges which covers all vertices of $G$. The anti-forcing number of $G$ is the smallest number of edges such that the remaining graph obtained by deleting these edges has a unique perfect matching and is denoted by $af(G)$. In this paper we consider some specifi...
متن کاملGlobal Forcing Number for Maximal Matchings under Graph Operations
Let $S= \{e_1,\,e_2, \ldots,\,e_m\}$ be an ordered subset of edges of a connected graph $G$. The edge $S$-representation of an edge set $M\subseteq E(G)$ with respect to $S$ is the vector $r_e(M|S) = (d_1,\,d_2,\ldots,\,d_m)$, where $d_i=1$ if $e_i\in M$ and $d_i=0$ otherwise, for each $i\in\{1,\ldots , k\}$. We say $S$ is a global forcing set for maximal matchings of $G$ if $...
متن کاملExistence and uniqueness of the solution for a general system of operator equations in $b-$metric spaces endowed with a graph
The purpose of this paper is to present some coupled fixed point results on a metric space endowed with two $b$-metrics. We shall apply a fixed point theorem for an appropriate operator on the Cartesian product of the given spaces endowed with directed graphs. Data dependence, well-posedness and Ulam-Hyers stability are also studied. The results obtained here will be applied to prove the existe...
متن کاملOn the zero forcing number of some Cayley graphs
Let Γa be a graph whose each vertex is colored either white or black. If u is a black vertex of Γ such that exactly one neighbor v of u is white, then u changes the color of v to black. A zero forcing set for a Γ graph is a subset of vertices Zsubseteq V(Γ) such that if initially the vertices in Z are colored black and the remaining vertices are colored white, then Z changes the col...
متن کامل