Results 221 to 230 of about 990,454 (252)

A Graph of Primes

Mathematics Magazine, 1993
Some time ago a colleague asked me a question about the graph formed by associating a vertex with each prime, and placing an edge between each pair of primes whose difference in absolute value is a nonnegative power of 2. His question was whether the graph formed in this way is connected.
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A new concept of primeness in graphs

Networks, 1981
AbstractA graph is quasiprime with respect to a boolean product of graphs if whenever it is a subgraph of the product of two graphs, it must necessarily be isomorphic to a subgraph of one of its factors. This paper provides a characterization of graphs quasi‐prime with respect to cartesian product, as well as graphs quasiprime with respect to other ...
Roger H. Lamprey, Bruce H. Barnes
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Colouring prime distance graphs

Graphs and Combinatorics, 1990
Let \(D\) be a set of prime numbers. The prime distance graph \(Z(D)\) is the graph with integers as vertex set, and an edge between \(x\) and \(y\) precisely when \(|x-y| \in D\). Easily one obtains for the chromatic number \(\chi(D)\) of \(Z(D)\) that \(\chi(D) \leq 4\).
Roger B. Eggleton, Paul Erdös, D. K. Skilton   +2 more
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On Factorable Extensions and Subgraphs of Prime Graphs

SIAM Journal on Discrete Mathematics, 1989
Summary: Cartesian-factorable extensions and subgraphs of prime graphs are investigated. It is shown that minimal factorable extensions and maximal factorable subgraphs are not unique and that finding them is NP-hard even, in the case of minimal factorable extensions, if the prime graph in question is required to be a tree.
Joan Feigenbaum, Ramsey W. Haddad
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On Prime Distance Labeling of Graphs

2017
A graph G is a prime distance graph if its vertices can be labeled with distinct integers in such a way that for any two adjacent vertices, the absolute difference of their labels is a prime number. It is known that cycles and bipartite graphs are prime distance graphs. In this paper we derive certain general results concerning prime distance labeling.
A. Parthiban, N. Gnanamalar David
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Degree prime graph

Journal of Discrete Mathematical Sciences and Cryptography, 2009
Abstract The degree prime graph DP(G) of a graph G is a graph having the same vertex set as G and two vertices are adjacent in DP(G) if and only if their degrees are unequal and relatively prime in G. In this paper, we obtain several properties of DP(G) and characterise graphs G which are isomorphic to DP(G).
M. Sattanathan, R. Kala
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Reducing prime graphs and recognizing circle graphs

Combinatorica, 1987
A reduction theorem for prime (simple) graphs in \textit{W. H. Cunningham}'s sense [SIAM J. Algebraic Discrete Methods 3, 214-228 (1982; Zbl 0497.05031)] is presented. It says that every prime graph of order \(n>5\) contains a smaller prime graph of order n-1.
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Vertex‐transitive graphs: Symmetric graphs of prime valency

Journal of Graph Theory, 1984
AbstractLet G be a group acting symmetrically on a graph Σ, let G1 be a subgroup of G minimal among those that act symmetrically on Σ, and let G2 be a subgroup of G1 maximal among those normal subgroups of G1 which contain no member except 1 which fixes a vertex of Σ. The most precise result of this paper is that if Σ has prime valency p, then either Σ
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Prime Testing for the Split Decomposition of a Graph

SIAM Journal on Discrete Mathematics, 1989
Summary: An \(O(n^ 2)\) algorithm for testing whether a graph is decomposable with respect to the split decomposition is developed. The fastest previous algorithm required \(\Omega (n^ 3)\) time for this problem. This leads to an \(O(n^ 2)\) expected time algorithm for computing the split decomposition of a graph.
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The N-Prime Graph Question is equivalent to the Prime Graph Question

Let $G$ be a finite group and let $V(\mathbb ZG)$ be the group of normalized units of its integral group ring. We prove that every $N$-prime arc of $V(\mathbb ZG)$ either already occurs in $G$ or admits commuting witnesses of distinct prime orders. Writing $A(Δ)$ for the arc set of a directed graph $Δ$, $E(Δ)$ for the edge set of an undirected graph ...
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