Extremal graphs with given order and the rupture degree
نویسندگان
چکیده
منابع مشابه
Diameter Two Graphs of Minimum Order with Given Degree Set
The degree set of a graph is the set of its degrees. Kapoor et al. [Degree sets for graphs, Fund. Math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. Furthermore, the minimum order of such a graph is determined. A graph is 2-self- centered if its radius and diameter are two. In this paper for ...
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the degree set of a graph is the set of its degrees. kapoor et al. [degree sets for graphs, fund. math. 95 (1977) 189-194] proved that for every set of positive integers, there exists a graph of diameter at most two and radius one with that degree set. furthermore, the minimum order of such a graph is determined. a graph is 2-self- centered if its radius and diameter are two. in this paper for ...
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متن کاملRupture degree of graphs
We introduce a new graph parameter, the rupture degree. The rupture degree for a complete graph Kn is defined as 1 − n, and the rupture degree for an incomplete connected graph G is defined by r(G) = max{ω(G − X)− |X| − m(G − X) : X ⊂ V(G),ω(G − X) > 1}, where ω(G − X) is the number of components of G − X and m(G − X) is the order of a largest component of G − X . It is shown that this paramete...
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It is now known that many properties of the objects in certain combinatorial structures are equivalent, in the sense that any object possessing any of the properties must of necessity possess them all. These properties, termed quasirandom, have been described for a variety of structures such as graphs, hypergraphs, tournaments, Boolean functions, and subsets of Zn, and most recently, sparse gra...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2010
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2010.07.001