the reliability wiener number of cartesian product graphs

نویسندگان

d. rupnik poklukar

j. zerovnik

چکیده

reliability wiener number is a modification of the original wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain conditions the bonds can break with certain probability. this is fully taken into account in quantum chemistry. in the model considered here, probabilistic nature is taken into account and at the same time the conceptual simplicity of the discrete graph theoretical model is preserved. here we extend previous studies by deriving a formula for the reliability wiener number of a cartesian product of graphs.

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

The reliability Wiener number of cartesian product graphs

Reliability Wiener number is a modification of the original Wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. Various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain condition...

متن کامل

On the reliability wiener number

One of the generalizations of the Wiener number to weighted graphs is to assign probabilities to edges, meaning that in nonstatic conditions the edge is present only with some probability. The Reliability Wiener number is defined as the sum of reliabilities among pairs of vertices, where the reliability of a pair is the reliability of the most reliable path. Closed expressions are derived for t...

متن کامل

Game Chromatic Number of Cartesian Product Graphs

The game chromatic number χg is considered for the Cartesian product G 2 H of two graphs G and H. We determine exact values of χg(G2H) when G and H belong to certain classes of graphs, and show that, in general, the game chromatic number χg(G2H) is not bounded from above by a function of game chromatic numbers of graphs G and H. An analogous result is proved for the game coloring number colg(G2...

متن کامل

K-tuple Chromatic Number of the Cartesian Product of Graphs

A k-tuple coloring of a graph G assigns a set of k colors to each vertex of G such that if two vertices are adjacent, the corresponding sets of colors are disjoint. The k-tuple chromatic number of G, χk(G), is the smallest t so that there is a k-tuple coloring of G using t colors. It is well known that χ(G2H) = max{χ(G), χ(H)}. In this paper, we show that there exist graphs G and H such that χk...

متن کامل

Hadwiger Number and the Cartesian Product of Graphs

The Hadwiger number η(G) of a graph G is the largest integer n for which the complete graph Kn on n vertices is a minor of G. Hadwiger conjectured that for every graph G, η(G) ≥ χ(G), where χ(G) is the chromatic number of G. In this paper, we study the Hadwiger number of the Cartesian product G H of graphs. As the main result of this paper, we prove that η(G1 G2) ≥ h √ l (1− o(1)) for any two g...

متن کامل

The edge geodetic number and Cartesian product of graphs

For a nontrivial connected graph G = (V (G), E(G)), a set S ⊆ V (G) is called an edge geodetic set of G if every edge of G is contained in a geodesic joining some pair of vertices in S. The edge geodetic number g1(G) of G is the minimum order of its edge geodetic sets. Bounds for the edge geodetic number of Cartesian product graphs are proved and improved upper bounds are determined for a speci...

متن کامل

منابع من

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


عنوان ژورنال:
iranian journal of mathematical chemistry

ناشر: university of kashan

ISSN 2228-6489

دوره 6

شماره 2 2015

میزبانی شده توسط پلتفرم ابری doprax.com

copyright © 2015-2023