Results 261 to 270 of about 33,385 (288)

Editing to Prime Graphs

Bulletin of the Malaysian Mathematical Sciences Society, 2021
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Houmem Belkhechine, Cherifa Ben Salha
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Finite prime distance graphs and 2-odd graphs

Discrete Mathematics, 2013
A graph $G$ is a prime distance graph (respectively, a 2-odd graph) if its vertices can be labeled with distinct integers such that for any two adjacent vertices, the difference of their labels is prime (either 2 or odd). We prove that trees, cycles, and bipartite graphs are prime distance graphs, and that Dutch windmill graphs and paper mill graphs ...
Joshua D Laison
exaly   +4 more sources

Hamiltonicity in Prime Sum Graphs

Graphs and Combinatorics, 2020
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Hong-Bin Chen, Hung-Lin Fu, Jun-Yi Guo
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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.
André Bouchet
exaly   +2 more sources

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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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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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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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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