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Prime Labelings of Snake Graphs
The PUMP Journal of Undergraduate Research, 2019 A prime labeling of a graph G with n vertices is a labeling of the vertices with distinct integers from the set {1, 2 ,..., n} such that the labels of any two adjacent vertices are relatively prime. In this paper, we introduce a snake graph, the fused union of identical cycles, and define a consecutive snake prime labeling for this new family of graphs.
Abigail Bigham +4 more
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Prime ideal graphs of commutative rings
Indonesian Journal of Combinatorics, 2022 Let R be a finite commutative ring with identity and P be a prime ideal of R. The vertex set is R - {0} and two distinct vertices are adjacent if their product in P. This graph is called the prime ideal graph of R and denoted by ΓP.
Haval Mohammed Salih, Asaad A. Jund
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𝒌𝒕𝒉 FIBONACCI PRIME LABELING OF SNAKE GRAPHS [PDF]
Journal of Mechanics of Continua and Mathematical Scienceskth Fibonacci Prime Labeling is defined as labeling the vertices of a graph with distinct Fibonacci numbers starting since the kth Fibonacci term sustaining the condition that the 𝑔𝑐𝑑(𝑓(𝑢), 𝑓(𝑣)) = 1, where 𝑓(𝑢) and 𝑓(𝑣) are labels of any adjacent ...
Anna S. Varghese +2 more
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PRIME LABELING OF AMALGAMATION OF FLOWER GRAPHS
BarekengGraph labeling is the assigning of labels represented by integers or symbols to graph elements, edges and/or vertices (or both) of a graph. Consider a simple graph with a vertex-set and an edge-set .
Desi Rahmadani +4 more
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Inverse Domination Parameters of Jump Graph
Ratio Mathematica, 2023 Let G=(V,E)\ be a connected graph. Let D be a minimum dominating set in G.\ If V-D contains a dominating set D^\prime of G, then D^\prime is called an inverse dominating set with respect to D.
S Santha, G.T Krishna Veni
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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 ...
Laison, Joshua D. +2 more
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On Minimal Prime Graphs and Posets [PDF]
Order, 2009 We show that there are four infinite prime graphs such that every infinite prime graph with no infinite clique embeds one of these graphs. We derive a similar result for infinite prime posets with no infinite chain or no infinite antichain.
Pouzet, Maurice, Zaguia, Imed
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The chromatic numbers of prime graphs of polynomials and power series over rings
AIMS MathematicsA prime graph of a ring $ R $, denoted by $ PG^*(R) $, is a graph whose vertex set is the set of the strong zero divisors $ S(R) $ of $ R $, and its edge set is either $ E(PG^*(R)) = \{ (x, y) : xRy = 0 $ or $ yRx = 0, x \neq y $ and $ x, y \in S(R) \} $
Walaa Alqarafi +2 more
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Some identities for enumerators of circulant graphs
, 2001 We establish analytically several new identities connecting enumerators of different types of circulant graphs of prime, twice prime and prime-squared orders.
Liskovets, Valery A.
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Prime Labeling of H- Super Subdivision of Y-tree Related Graphs
Ratio Mathematica, 2023 A graph G with p points is called a prime labeling , if it possible to label the points x 2 V with distinct labels f(x) from f1;2; :::; pg in such a way that for each line e = uv gcd (f(u); f(v)) = 1 .
Meena S, Gajalakshmiy G
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