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Edge-neighbor-integrity of trees

1994
*
The Australasian Journal of Combinatorics
*

In this paper, we find the minimum and maximum edge-

dblp:journals/ajc/CozzensW94
fatcat:olsf6mdsqbdrlej4navbwehccq
*neighbor*-*integrity*among all*trees*with any fixed order, and also show that for any integer I between the extreme values there is a*tree*with the edge-*neighbor*-*integrity*... The edge-*neighbor*-*integrity**of*a graph G, ENI(G), is defined to be ENI(G) = min {lSI + w(G/S)}, where S is any edge subversion strategy*of*G, and w(G/S) is the maximum order*of*the components*of*GIS. ... If we can find a*tree**of*order at least 3 whose edge-*neighbor*-*integrity*is 2, then the minimum edge-*neighbor*-*integrity*among all*trees*is 2. QED. ...##
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Discrete SIR model on a homogeneous tree and its continuous limit
[article]

2022
*
arXiv
*
pre-print

We study a discrete Susceptible-Infected-Recovered (SIR) model for the spread

arXiv:2005.04743v5
fatcat:aa25zcx6hbaade4ojippx5yumm
*of*infectious disease on a homogeneous*tree*and the limit behavior*of*the model in the case when the*tree**vertex*degree tends ... We obtain the distribution*of*the time it takes for a susceptible*vertex*to get infected in terms*of*a solution*of*a non-linear*integral*equation under broad assumptions on the model parameters. ... Further, recall that a rooted homogeneous*tree*with the*vertex*degree N ≥ 2 as a*tree*, where one*of*the vertices, called the root, has N − 1*neighbors*, while any other*vertex*has N*neighbors*. ...##
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Vertex-neighbor-integrity of magnifiers, expanders, and hypercubes

2000
*
Discrete Mathematics
*

The

doi:10.1016/s0012-365x(99)00352-0
fatcat:fa5fteyig5c6je5hxcxw62g4x4
*vertex*-*neighbor*-*integrity**of*G is deÿned to be VNI is the order*of*the largest connected component in the graph H . ... Finally, we show that the decision problem corresponding to computing the*vertex*-*neighbor*-*integrity**of*a graph is NP-complete. ... This research was done while the author was an undergraduate at the University*of*Chicago under the supervision*of*Joseph Gallian at the 1998 Summer Research Program at the University*of*Minnesota, Duluth ...##
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Integral trees with given nullity
[article]

2015
*
arXiv
*
pre-print

A graph is called

arXiv:1207.1802v2
fatcat:wixa5addwbc6derhyf4nlxkuzi
*integral*if all eigenvalues*of*its adjacency matrix consist entirely*of*integers. We prove that for a given nullity more than 1, there are only finitely many*integral**trees*. ... It is also shown that*integral**trees*with nullity 2 and 3 are unique. ... Acknowledgments The authors are indebted to an anonymous referee for pointing out an error in the proof*of*the main result in an earlier version*of*the manuscript. ...##
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A linear delay algorithm for enumerating all connected induced subgraphs

2019
*
BMC Bioinformatics
*

To efficiently mine all maximal cohesive subgraphs, we propose two pruning techniques that remove futile search nodes in the enumeration

doi:10.1186/s12859-019-2837-y
fatcat:wvfiqia3ijfxtcgt2om56dniia
*tree*. ... Building on this enumeration approach, we propose an algorithm for mining all maximal cohesive subgraphs that*integrates*vertices' attributes with subgraph enumeration. ... Availability*of*data and materials The dataset and the implementation*of*the algorithm is available at http:// www.cs.ndsu.nodak.edu/~ssalem/multirelation.html. About this supplement ...##
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The integrally representable trees of norm 3
[article]

2016
*
arXiv
*
pre-print

In this paper, we determine the

arXiv:1612.06971v1
fatcat:ahwrfueannazlewfz26mussw6a
*integrally*representable*trees**of*norm 3. ... (ii) If h contains a slim*vertex*with at least two fat*neighbors*, then h is*integrally*representable*of*norm 3. 3*Tree*-like Hoffman graphs Stripped Hoffman graphs Let t 1 and t 2 be two*tree*-like Hoffman ... For a*vertex*x*of*h, we define N s h (x) (resp. N f h (x) ) the set*of*slim (resp. fat)*neighbors**of*x in h. If every slim*vertex**of*the Hoffman graph h has a fat*neighbor*, then we call h fat. ...##
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The integrally representable trees of norm $3$

2017
*
Annals of Mathematical Sciences and Applications
*

For a 3-seedling t with ψ as its reduced representation

doi:10.4310/amsa.2017.v2.n2.a7
fatcat:kjbupncmy5bkjic4cxfiajyzxu
*of*norm 3, let Λ red (t, 3) be the lattice generated by vectors ψ(x) with x ∈ V s (h). Problem 2. ... Recall from [4] that an*integral*lattice Λ is s-*integrable*, for a positive integer s, if it can be described by vectors s − 1 2 (x 1 , . . . , x n ) with all x i ∈ Z. ... (ii) If h contains a slim*vertex*with at least two fat*neighbors*, then h is*integrally*representable*of*norm 3. Lemma 3 . 4 . 34 Let T = (T, sgn) be an edge-signed*tree*. ...##
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Integral trees with given nullity

2016
*
Discrete Mathematics
*

A graph is called

doi:10.1016/j.disc.2015.08.007
fatcat:klewytrgp5h4nglvx6ncymbcze
*integral*if all eigenvalues*of*its adjacency matrix consist entirely*of*integers. We prove that for a given nullity more than 1, there are only finitely many*integral**trees*. ...*Integral**trees*with nullity at most 1 were already characterized by Watanabe and Brouwer. It is shown that*integral**trees*with nullity 2 and 3 are unique. ... Acknowledgments The authors are indebted to an anonymous referee for pointing out an error in the proof*of*the main result in an earlier version*of*the manuscript. ...##
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Statistics of planar graphs viewed from a vertex: a study via labeled trees

2003
*
Nuclear Physics B
*

We study the statistics

doi:10.1016/j.nuclphysb.2003.09.046
fatcat:zjniw2xfbneupkuek6hrpu43da
*of*edges and vertices in the vicinity*of*a reference*vertex*(origin) within random planar quadrangulations and Eulerian triangulations. ... In the case*of*infinitely large graphs, we give in particular explicit formulas for the probabilities that the origin have given numbers*of**neighboring*edges and/or vertices, as well as explicit values ... For each*vertex**of*the*tree*reaching position 1, we have an energy gain ρα k , where k is the number*of*nearest*neighbors**of*the*vertex*on the*tree*. ...##
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Bijective Deformations in R^n via Integral Curve Coordinates
[article]

2015
*
arXiv
*
pre-print

We introduce

arXiv:1505.00073v1
fatcat:p6hb2g4atzhd3b7napsg5fkabq
*Integral*Curve Coordinates, which identify each point in a bounded domain with a parameter along an*integral*curve*of*the gradient*of*a function f on that domain; suitable functions have exactly ... Because every*integral*curve intersects the boundary exactly once,*Integral*Curve Coordinates provide a natural bijective mapping from one domain to another given a bijection*of*the boundary. ... Cousin*tree**vertex*relationships: Two vertices u, v that are axis-aligned*neighbors*in the grid must be either parent-child (left) or*tree*cousins (right). ...##
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Implementation Of Heuristics For Solving Travelling Salesman Problem Using Nearest Neighbour And Minimum Spanning Tree Algorithms

2013
*
Zenodo
*

This paper adopts the nearest

doi:10.5281/zenodo.1088389
fatcat:fgr2squuizcqzo4f3ermnqkuuu
*neighbor*and minimum spanning*tree*algorithm to solve the well-known travelling salesman problem. The algorithms were implemented using java programming language. ... The approach is tested on three graphs that making a TSP tour instance*of*5-city, 10 –city, and 229–city. The computation results validate the performance*of*the proposed algorithm. ... The root*of*the*tree*is the start*vertex*or point in the tour. First we iterate over the root's*neighbors*; for each*neighbor*w, we add the edge triple <root, w, weight> to the priority queue. ...##
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RAG: RNA-As-Graphs web resource

2004
*
BMC Bioinformatics
*

All RNA motifs are filed according to their graph

doi:10.1186/1471-2105-5-88
pmid:15238163
pmcid:PMC471545
fatcat:4crxaf6q5bavvf45tina55iyj4
*vertex*number (RNA length) and ranked by topological complexity. ... The proliferation*of*structural and functional studies*of*RNA has revealed an increasing range*of*RNA's structural repertoire. ... Fera acknowledges support from the Dean's Undergraduate Research Fund and a summer fellowship from the Department*of*Chemistry. ...##
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Walks and regular integral graphs

2007
*
Linear Algebra and its Applications
*

in an infinite regular

doi:10.1016/j.laa.2006.11.026
fatcat:piiylzih2vd2xn6aendplhulbi
*tree*, provides a lower bound on the number*of*closed walks in regular graphs. ... This lower bound is then applied to reduce the number*of*the feasible spectra*of*the 4-regular bipartite*integral*graphs by more than a half. ... It is homomorphic by its construction, since the*neighbors**of*any*vertex*u ∈ V (B r ) are mapped to the*neighbors**of*f (u) in G. ...##
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Acquisition-extremal graphs

2013
*
Discrete Applied Mathematics
*

three edges from

doi:10.1016/j.dam.2012.12.014
fatcat:dypjcl43zvd6plyzejsm7bwaqq
*neighbors**of*leaves. ... A total acquisition move in a weighted graph G moves all weight from a*vertex*u to a*neighboring**vertex*v, provided that before this move the weight on v is at least the weight on u. ... By definition, every non-leaf*vertex**of*a*tree*is a core*vertex*or has a leaf*neighbor*. ...##
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Power Optimization in Fault-Tolerant Topology Control Algorithms for Wireless Multi-hop Networks

2007
*
IEEE/ACM Transactions on Networking
*

Specifically, we require all links established by this power setting be symmetric and form a k-

doi:10.1109/tnet.2007.902680
fatcat:g5y2t432pjgcndlkjkvdv7rbfy
*vertex*connected subgraph*of*the network graph. This problem is known to be NP-hard. ... Our third algorithm assumes that the edge lengths*of*the network graph form a metric. ... In the optimal*integral*solution, there should be at least one edge incident to each*vertex*; thus the cost*of*an optimal*integral*solution is at least n since p v ≥ 1 for all v. ...
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