The Merrifield-Simmons Conjecture Holds for Bipartite Graphs

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On a conjecture of Merrifield and Simmons

On page 144 of (3], a (see Gutman[l]), formulated as follows:

متن کامل

Tricyclic graphs with maximum Merrifield-Simmons index

It is well known that the graph invariant, ‘the Merrifield–Simmons index’ is important one in structural chemistry. The connected acyclic graphs with maximal and minimal Merrifield–Simmons indices are determined by Prodinger and Tichy [H. Prodinger, R.F. Tichy, Fibonacci numbers of graphs, Fibonacci Quart. 20 (1982) 16–21]. The sharp upper and lower bounds for theMerrifield–Simmons indices of u...

متن کامل

Algorithmic generation of molecular graphs with large Merrifield-Simmons index

The Merrifield-Simmons index is related to several physicochemical characteristics and is thus of use in combinatorial chemistry, e.g. in drug design and molecular recognitions. In this paper, we show how one can algorithmically construct databases of acyclic molecular graphs with large Merrifield-Simmons index. Our algorithm can deal with a large number of atoms (several hundreds) in short tim...

متن کامل

Graphs with maximal Hosoya index and minimal Merrifield-Simmons index

For a graph G, the Hosoya index and the Merrifield-Simmons index are defined as the total number of its matchings and the total number of its independent sets, respectively. In this paper, we characterize the structure of those graphs that minimize the Merrifield-Simmons index and those that maximize the Hosoya index in two classes of simple connected graphs with n vertices: graphs with fixed m...

متن کامل

The union-closed sets conjecture almost holds for almost all random bipartite graphs

Frankl’s union-closed sets conjecture states that in every finite unionclosed family of sets, not all empty, there is an element in the ground set contained in at least half of the sets. The conjecture has an equivalent formulation in terms of graphs: In every bipartite graph with least one edge, both colour classes contain a vertex belonging to at most half of the maximal stable sets. We prove...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Graph Theory

سال: 2012

ISSN: 0364-9024

DOI: 10.1002/jgt.21656