منابع مشابه
Labeled embedding of (n, n-2)-graphs in their complements
21 Graph packing generally deals with unlabeled graphs. In [4], the authors 22 have introduced a new variant of the graph packing problem, called the 23 labeled packing of a graph. This problem has recently been studied on trees 24 [6] and cycles [4]. In this note, we present a lower bound on the labeled 25 packing number of any (n, n − 2)-graph into Kn. This result improves the 26 bound given ...
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A graph H is a minor of a graph G if H can be obtained from a subgraph of G by contracting edges. Let t ≥ 1 be an integer, and let G be a graph on n vertices with no minor isomorphic to Kt+1. Kostochka conjectures that there exists a constant c = c(k) independent of G such that the complement of G has a minor isomorphic to Ks, where s = d2 (1 + 1/t)n − ce. We prove that Kostochka’s conjecture i...
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Given a graph G; let kGk denote the trace norm of its adjacency matrix, also known as the energy of G: The main result of this paper states that if G is a graph of order n; then kGk + G (n 1) 1 +n ; where G is the complement of G: Equality is possible if and only if G is a strongly regular graph with parameters (n; (n 1) =2; (n 5) =4; (n 1) =4) ; known also as a conference graph. In fact, the a...
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In this paper the authors study the edge-integrity of graphs. Edge-integrity is a very useful measure of the vulnerability of a network, in particular a communication network, to disruption through the deletion of edges. A number of problems are examined, including some Nordhaus-Gaddum type results. Honest graphs, i.e. those which have the maximum possible edge-integrity, are also investigated....
متن کاملRepresentations of Split Graphs , Their Complements , Stars , and Hypercubes
A graph G has a representation modulo n if there exists an injective map f : V (G) → {0, 1, . . . , n} such that vertices u and v are adjacent if and only if |f(u) − f(v)| is relatively prime to n. The representation number rep(G) is the smallest n such that G has a representation modulo n. We present new results involving representation numbers for stars, split graphs, complements of split gra...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1981
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1981.101722