Results 1  10
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SUBGRAPHS OF COMPLETE GRAPH
"... Abstract: In the complete graph K2m+3 for m ≥ 2, we study some structures of simple nonisomorphic Hamiltonian subgraphs of the form H ( 2m+3, 6m+3) for m ≥ 2. The various structures of the form H(2m+3, 6m+3) for m ≥ 2 are found and some of them are observed to give some forms of metal atom cluster ..."
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Abstract: In the complete graph K2m+3 for m ≥ 2, we study some structures of simple nonisomorphic Hamiltonian subgraphs of the form H ( 2m+3, 6m+3) for m ≥ 2. The various structures of the form H(2m+3, 6m+3) for m ≥ 2 are found and some of them are observed to give some forms of metal atom
ENUMERATION OF WEIGHTED COMPLETE GRAPHS
"... Abstract. We enumerate the number of weighted complete graphs and compute its generating function. 1. ..."
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Abstract. We enumerate the number of weighted complete graphs and compute its generating function. 1.
COMPLETE GRAPHS AND SMALL GRAPHS WITH STRICT
, 2013
"... The combinatorial inverse eigenvalue problems: complete graphs and small graphs with strict inequality ..."
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The combinatorial inverse eigenvalue problems: complete graphs and small graphs with strict inequality
Geometric Thickness of Complete Graphs
 J. GRAPH ALGORITHMS APPL
, 2000
"... We define the geometric thickness of a graph to be the smallest number of layers such that we can draw the graph in the plane with straightline edges and assign each edge to a layer so that no two edges on the same layer cross. The geometric thickness lies between two previously studied quantiti ..."
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Cited by 32 (4 self)
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quantities, the (graphtheoretical) thickness and the book thickness. We investigate the geometric thickness of the family of complete graphs, {Kn}. We show that the geometric thickness of Kn lies between #(n/5.646) + 0.342# and #n/4#, and we give exact values of the geometric thickness of Kn for n
The Order Dimension of the Complete Graph
 DISCRETE MATH
, 1998
"... We show that the order dimension of the complete graph on n vertices is the smallest integer t for which there are n antichains in the subset lattice of [t  1] that do not contain [t  1] or two sets whose union is [t  1]. ..."
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Cited by 9 (0 self)
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We show that the order dimension of the complete graph on n vertices is the smallest integer t for which there are n antichains in the subset lattice of [t  1] that do not contain [t  1] or two sets whose union is [t  1].
Layered percolation on the complete graph
, 2009
"... ABSTRACT. We present a generalized (multitype) version of percolation on the complete graph, in which we divide the vertices of the graph into a fixed number of sets (called layers) and perform percolation where the probability of {u, v} being in our edge set depends on the respective layers of u an ..."
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Cited by 2 (0 self)
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ABSTRACT. We present a generalized (multitype) version of percolation on the complete graph, in which we divide the vertices of the graph into a fixed number of sets (called layers) and perform percolation where the probability of {u, v} being in our edge set depends on the respective layers of u
On CliqueComplete Graphs
 Discrete Math
, 1992
"... A graph is cliquecomplete if no two of its maximal cliques are disjoint. A vertex is universal if it is adjacent to all other vertices in the graph. We prove that every cliquecomplete graph either contains a universal vertex or an induced subgraph in an indexed family Q := fQ 2n+1 : n 1g, defined ..."
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A graph is cliquecomplete if no two of its maximal cliques are disjoint. A vertex is universal if it is adjacent to all other vertices in the graph. We prove that every cliquecomplete graph either contains a universal vertex or an induced subgraph in an indexed family Q := fQ 2n+1 : n 1g
ON SWELL–COLORED COMPLETE GRAPHS
, 1994
"... Abstract. An edgecolored graph is said to be swellcolored if each triangle contains exactly 1 or 3 colors but never 2 colors and if the graph contains more than one color. It is shown that a swellcolored complete graph with n vertices contains at least √ n + 1 colors. The complete graph with n2 v ..."
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Abstract. An edgecolored graph is said to be swellcolored if each triangle contains exactly 1 or 3 colors but never 2 colors and if the graph contains more than one color. It is shown that a swellcolored complete graph with n vertices contains at least √ n + 1 colors. The complete graph with n2
Partial profiles of quasicomplete graphs
, 2008
"... We enumerate graph homomorphisms to quasicomplete graphs i.e., graphs obtained from complete graphs by removing one edge. The source graphs are complete graphs, quasicomplete graphs, cycles, paths, wheels and broken wheels. ..."
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We enumerate graph homomorphisms to quasicomplete graphs i.e., graphs obtained from complete graphs by removing one edge. The source graphs are complete graphs, quasicomplete graphs, cycles, paths, wheels and broken wheels.
Hypergraceful Complete Graphs
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 48 (2010), PAGES 5–24
, 2010
"... In this paper we prove that no signed graph on the complete graph Kp, p ≥ 6, is graceful, and we also give a characterization of graceful signed graphs on Kp, p ≤ 5. This implies that there is no subset A of cardinality p ≥ 6fromtheset{0, 1,..., ( ) () p 1 p − n}, n ≤ , such that each 2 2 2 elemen ..."
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In this paper we prove that no signed graph on the complete graph Kp, p ≥ 6, is graceful, and we also give a characterization of graceful signed graphs on Kp, p ≤ 5. This implies that there is no subset A of cardinality p ≥ 6fromtheset{0, 1,..., ( ) () p 1 p − n}, n ≤ , such that each 2 2 2
Results 1  10
of
10,744