Maximal Hosoya index and extremal acyclic molecular graphs without perfect matching
نویسندگان
چکیده
منابع مشابه
Maximal Hosoya index and extremal acyclic molecular graphs without perfect matching
Let T be an acyclic graph without perfect matching and Z(T ) be its Hosoya index; let Fn be the nth Fibonacci number. It is proved in this work that Z(T ) ≤ 2F2m F2m+1 when T has order 4m with the equality holding if and only if T = T1,2m−1,2m−1, and that Z(T ) ≤ F2 2m+2 + F2m F2m+1 when T has order 4m + 2 with the equality holding if and only if T = T1,2m+1,2m−1, where m is a positive integer ...
متن کاملGraphs 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 کاملEccentric Connectivity Index: Extremal Graphs and Values
Eccentric connectivity index has been found to have a low degeneracy and hence a significant potential of predicting biological activity of certain classes of chemical compounds. We present here explicit formulas for eccentric connectivity index of various families of graphs. We also show that the eccentric connectivity index grows at most polynomially with the number of vertices and determine ...
متن کاملOn acyclic systems with minimal Hosoya index
The Hosoya index of a graph is de*ned as the total number of independent edge subsets of the graph. In this note, we characterize the trees with a given size of matching and having minimal and second minimal Hosoya index. ? 2002 Elsevier Science B.V. All rights reserved.
متن کاملSome extremal unicyclic graphs with respect to Hosoya index and Merrifield-Simmons index
The Hosoya index of a graph is defined as the total number of the matchings, including the empty edge set, of the graph. The Merrifield-Simmons index of a graph is defined as the total number of the independent vertex sets, including the empty vertex set, of the graph. Let U(n,∆) be the set of connected unicyclic graphs of order n with maximum degree ∆. We consider the Hosoya indices and the Me...
متن کاملذخیره 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: Applied Mathematics Letters
سال: 2006
ISSN: 0893-9659
DOI: 10.1016/j.aml.2005.08.017