منابع مشابه
Average Distance and Independence Number
A sharp upper bound on the average distance of a graph depending on the order and the independence number is given. As a corollary we obtain the maximum average distance of a graph with given order and matching number. All extremal graphs are determined.
متن کاملThe Average Lower Independence Number of Total Graphs
In communication networks, ”vulnerability” indicates the resistance of a network to disruptions in communication after a breakdown of some processors or communication links. We may use graphs to model networks, as graph theoretical parameters can be used to describe the stability and reliability of communication networks If we think of a graph as modeling a network, the average lower independen...
متن کاملOn the Average Lower Independence Number of Some Graphs
In a communication network, several vulnerability measures are used to determine the resistance of the network to disruption of operation after the failure of certain stations or communication links. If the communication network is modeled as a simple, undirected, connected and unweighted graph G, then average lower independence number of a graph G can be considered as a measure of graph vulner...
متن کاملAverage independence polynomials
The independence polynomial of a graph G is the function i(G, x) = ∑k 0 ikx , where ik is the number of independent sets of vertices in G of cardinality k. We investigate here the average independence polynomial, where the average is taken over all independence polynomials of (labeled) graphs of order n. We prove that while almost every independence polynomial has a nonreal root, the average in...
متن کاملIndependence, odd girth, and average degree
We prove several best-possible lower bounds in terms of the order and the average degree for the independence number of graphs which are connected and/or satisfy some odd girth condition. Our main result is the extension of a lower bound for the independence number of triangle-free graphs of maximum degree at most 3 due to Heckman and Thomas [A New Proof of the Independence Ratio of Triangle-Fr...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1994
ISSN: 0166-218X
DOI: 10.1016/0166-218x(94)90095-7