scholarly journals Central vertex join and central edge join of two graphs

2020 ◽  
Vol 5 (6) ◽  
pp. 7214-7233
Author(s):  
Jahfar T K ◽  
◽  
Chithra A V
Keyword(s):  
Central Vertex

scholarly journals The Class of q-Cliqued Graphs: Eigen-Bi-Balanced Characteristic, Designs, and an Entomological Experiment

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Paul August Winter ◽  
Carol Lynne Jessop ◽  
Costas Zachariades
Keyword(s):  
Central Vertex ◽  
Conjugate Pair ◽  
New Class

Much research has involved the consideration of graphs which have subgraphs of a particular kind, such as cliques. Known classes of graphs which are eigen-bi-balanced, that is, they have a pair a, b of nonzero distinct eigenvalues, whose sum and product are integral, have been investigated. In this paper we will define a new class of graphs, called q-cliqued graphs, on q2+1 vertices, which contain q cliques each of order q connected to a central vertex, and then prove that these q-cliqued graphs are eigen-bi-balanced with respect to a conjugate pair whose sum is -1 and product 1-q. These graphs can be regarded as design graphs, and we use a specific example in an entomological experiment.

scholarly journals FOLDING EQUILATERAL PLANE GRAPHS

2013 ◽  
Vol 23 (02) ◽  
pp. 75-92 ◽  
Author(s):  
ZACHARY ABEL ◽  
ERIK D. DEMAINE ◽  
MARTIN L. DEMAINE ◽  
SARAH EISENSTAT ◽  
JAYSON LYNCH ◽  
...  
Keyword(s):  
Plane Graph ◽  
Analogous Problem ◽  
Central Vertex ◽  
Polyhedral Complex ◽  
Plane Graphs ◽  
Single Vertex ◽  
Np Completeness ◽  
Np Complete ◽  
Polyhedral Manifold

We consider two types of folding applied to equilateral plane graph linkages. First, under continuous folding motions, we show how to reconfigure any linear equilateral tree (lying on a line) into a canonical configuration. By contrast, it is known that such reconfiguration is not always possible for linear (nonequilateral) trees and for (nonlinear) equilateral trees. Second, under instantaneous folding motions, we show that an equilateral plane graph has a noncrossing linear folded state if and only if it is bipartite. Furthermore, we show that the equilateral constraint is necessary for this result, by proving that it is strongly NP-complete to decide whether a (nonequilateral) plane graph has a linear folded state. Equivalently, we show strong NP-completeness of deciding whether an abstract metric polyhedral complex with one central vertex has a noncrossing flat folded state. By contrast, the analogous problem for a polyhedral manifold with one central vertex (single-vertex origami) is only weakly NP-complete.

A note on locating a central vertex of a 3-cactus graph

1990 ◽  
Vol 17 (3) ◽  
pp. 315-320 ◽  
Author(s):  
Rex K. Kincaid ◽  
Oded Z. Maimon
Keyword(s):  
Central Vertex ◽  
Cactus Graph

Characterizations of Three Classes of Zero-Divisor Graphs

2012 ◽  
Vol 55 (1) ◽  
pp. 127-137 ◽  
Author(s):  
John D. LaGrange
Keyword(s):  
Commutative Ring ◽  
Direct Product ◽  
Zero Divisor ◽  
Commutative Rings ◽  
Central Vertex ◽  
Integral Domains ◽  
Boolean Rings ◽  
Zero Divisor Graph ◽  
Zero Divisors

AbstractThe zero-divisor graph Γ(R) of a commutative ring R is the graph whose vertices consist of the nonzero zero-divisors of R such that distinct vertices x and y are adjacent if and only if xy = 0. In this paper, a characterization is provided for zero-divisor graphs of Boolean rings. Also, commutative rings R such that Γ(R) is isomorphic to the zero-divisor graph of a direct product of integral domains are classified, as well as those whose zero-divisor graphs are central vertex complete.

scholarly journals Some families of 0-rotatable graceful caterpillars

2018 ◽  
Author(s):  
Atílio G. Luiz ◽  
C. N. Campos ◽  
R. Bruce Richter
Keyword(s):  
Perfect Matching ◽  
Central Vertex ◽  
Injective Function

A graceful labelling of a tree T is an injective function f: V (T) → {0, 1, . . . , |E(T)|} such that {|f(u)−f(v)|: uv ∈ E(T)} = {1, 2, . . . , |E(T)|}. A tree T is said to be 0-rotatable if, for any v ∈ V (T), there exists a graceful labelling f of T such that f(v) = 0. In this work, it is proved that the follow- ing families of caterpillars are 0-rotatable: caterpillars with perfect matching; caterpillars obtained by identifying a central vertex of a path Pn with a vertex of K2; caterpillars obtained by identifying one leaf of the star K1,s−1 to a leaf of Pn, with n ≥ 4 and s ≥ ⌈n−1 2 ⌉; caterpillars with diameter five or six; and some families of caterpillars with diameter at least seven. This result reinforces the conjecture that all caterpillars with diameter at least five are 0-rotatable.  

scholarly journals Design Thinking on δ-Dynamic Coloring of Central Vertex Join of Graphs

2021 ◽  
Vol 1947 (1) ◽  
pp. 012057
Author(s):  
G. Nandini ◽  
V. Sandhya ◽  
A. Viswanathan
Keyword(s):  
Design Thinking ◽  
Central Vertex ◽  
Join Of Graphs

scholarly journals Finding a central vertex in an HHD-free graph

2003 ◽  
Vol 131 (1) ◽  
pp. 93-111 ◽  
Author(s):  
Victor Chepoi ◽  
Feodor Dragan
Keyword(s):  
Central Vertex ◽  
Free Graph

scholarly journals Reconstruction of the Sturm-Liouville operators on a graph with $\delta'_s$ couplings

2011 ◽  
Vol 42 (3) ◽  
pp. 329-342 ◽  
Author(s):  
ChuanFu Yang
Keyword(s):  
Uniqueness Theorem ◽  
Liouville Operator ◽  
Dense Subset ◽  
Star Graph ◽  
Central Vertex ◽  
Inverse Nodal Problems ◽  
Sturm Liouville ◽  
The Given ◽  
The Uniqueness Theorem ◽  
Liouville Operators

Inverse nodal problems consist in constructing operators from the given zeros of their eigenfunctions. In this work, we deal with the inverse nodal problems of reconstructing the Sturm- Liouville operator on a star graph with $\delta'_s $ couplings at the central vertex. The uniqueness theorem is proved and a constructive procedure for the solution is provided from a dense subset of zeros of the eigenfunctions for the problem as a data.

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