Extremal graphs having no matching cuts
نویسندگان
چکیده
A graph G = (V, E) is matching immune if there is no matching cut in G. We show that for any matching immune graph G, |E| ≥ ⌈3(|V | − 1)/2⌉. This bound is tight, as we define operations that construct, from a given vertex, exactly the class of matching immune graphs that attain the bound.
منابع مشابه
A characterization of extremal graphs without matching-cuts
A graph is called (matching-)immune if it has no edge cut that is also a matching. Farley and Proskurowski proved that for all immune graphs G = (V, E), |E| ≥ 3(|V |−1)/2 , and constructed a large class of immune graphs attaining this lower bound for every value of |V (G)|, called ABC graphs. In this paper, we prove their conjecture that every immune graph that attains this lower bound is an AB...
متن کاملThe Minimal Matching Energy of (n,m)-Graphs with a Given Matching Number
The matching energy of a graph is defined as the sum of the absolute values of the zeros of its matching polynomial. Let Gn,m be the set of connected graphs of order n and with m edges. In this note we determined the extremal graphs from Gn,m with n ≤ m ≤ 2n−4 minimizing the matching energy. Also we determined the minimal matching energy of graphs from Gn,m where m = n−1+t and 1 ≤ t ≤ β−1 and w...
متن کاملIncidence cuts and connectivity in fuzzy incidence graphs
Fuzzy incidence graphs can be used as models for nondeterministic interconnection networks having extra node-edgerelationships. For example, ramps in a highway system may be modeled as a fuzzy incidence graph so that unexpectedflow between cities and highways can be effectively studied and controlled. Like node and edge connectivity in graphs,node connectivity and arc connectivity in fuzzy inci...
متن کاملMatching Integral Graphs of Small Order
In this paper, we study matching integral graphs of small order. A graph is called matching integral if the zeros of its matching polynomial are all integers. Matching integral graphs were first studied by Akbari, Khalashi, etc. They characterized all traceable graphs which are matching integral. They studied matching integral regular graphs. Furthermore, it has been shown that there is no matc...
متن کاملZagreb, Harary and hyper-Wiener indices of graphs with a given matching number
In this paper, we present sharp bounds for the Zagreb indices, Harary index and hyperWiener index of graphs with a given matching number, and we also completely determine the extremal graphs. © 2010 Elsevier Ltd. All rights reserved.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Journal of Graph Theory
دوره 69 شماره
صفحات -
تاریخ انتشار 2012