منابع مشابه
On maximally irregular graphs
Let G be a connected graph with maximum degree ∆(G). The irregularity index t(G) of G is defined as the number of distinct terms in the degree sequence of G. We say that G is maximally irregular if t(G) = ∆(G). The purpose of this note, apart from pointing out that every highly irregular graph is maximally irregular, is to establish upper bounds on the size of maximally irregular graphs and max...
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Given a graph H, we say a graph G is H-saturated if G does not contain H as a subgraph and the addition of any edge e′ 6∈ E(G) results in H as a subgraph. In this paper, we construct (K4 − e)-saturated graphs with |E(G)| either the size of a complete bipartite graph, a 3-partite graph, or in the interval [ 2n− 4, ⌊ n 2 ⌋ ⌈ n 2 ⌉ − n+ 6 ] . We then extend the (K4−e)-saturated graphs to (Kt − e)-...
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Preface Graphs are often used as a model for networks, for example transport networks, telecommunication systems, a network of servers and so on. Typically, the networks and thus the representing graphs are connected; that means, that there exists a path between all pairs of two vertices in the graph. But sometimes an element of the network fails, for the graphs that means the removal of a vert...
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A graph is Ramsey unsaturated if there exists a proper supergraph of the same order with the same Ramsey number, and Ramsey saturated otherwise. This has been studied by Balister, Lehel and Schelp [J. Graph Theory 51 (2006), 22–32]. In this paper, we show that some circulant graphs, trees with diameter 3, and Kt,n ∪ mK1 for infinitely many t, n and m, are Ramsey unsaturated.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1982
ISSN: 0012-365X
DOI: 10.1016/0012-365x(82)90200-x