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Hamiltonicity in Prime Sum Graphs
Graphs and Combinatorics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hong-Bin Chen, Hung-Lin Fu, Jun-Yi Guo
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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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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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Colouring prime distance graphs
Graphs and Combinatorics, 1990Let \(D\) 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 \(\chi(D) \leq 4\).
Eggleton, R. B. +2 more
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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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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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Vertex‐transitive graphs: Symmetric graphs of prime valency
Journal of Graph Theory, 1984AbstractLet 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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Reducing prime graphs and recognizing circle graphs
Combinatorica, 1987A 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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Journal of Advanced Research in Dynamical and Control Systems, 2020
Simaringa M, Santhoshkumar K
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Simaringa M, Santhoshkumar K
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment
Ca-A Cancer Journal for Clinicians, 2022Jun J Mao,, Msce +2 more
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k-PRIME TOTAL LABELING OF GRAPHS
Advances and Applications in Discrete Mathematics, 2022Arockiamary, S. Teresa +2 more
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