نتایج جستجو برای: integral graph

تعداد نتایج: 310432  

2005
Ligong Wang

A graph G is called integral if all zeros of the characteristic polynomial P (G, x) are integers. Our purpose is to determine or to characterize which graphs are integral. This problem was posed by Harary and Schwenk in 1974. In general, the problem of characterizing integral graphs seems to be very difficult. Thus, it makes sense to restrict our investigations to some interesting families of g...

Journal: :Discrete Mathematics 2004
Ligong Wang Xueliang Li Cornelis Hoede

A graph is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper, we give a useful sufficient and necessary condition for complete r-partite graphs to be integral, from which we can construct infinite many new classes of such integral graphs. It is proved that the problem of finding such integral graphs is equivalent to the problem of solving some Diophantin...

2010
PAVEL H́IC

A graph G is called integral if all the eigenvalues of its adjacency matrix are integers. In this paper we investigate integral complete r−partite graphs Kp1,p2,...,pr = Ka1p1,a2p2,...,asps with s ≤ 4. New sufficient conditions for complete 3-partite graphs and complete 4-partite graphs to be integral are given. From these conditions we construct infinitely many new classes of integral complete...

Journal: :Annals of Combinatorics 2021

Motivated by the notion of chip-firing on dual graph a planar graph, we consider ‘integral flow chip-firing’ an arbitrary G. The rule is governed $${\mathcal {L}}^*(G)$$ , Laplacian G determined choosing basis for lattice integral flows We show that any admits such so M-matrix, leading to firing these elements avalanche finite. This follows from more general result bases lattices may be indepen...

پایان نامه :وزارت علوم، تحقیقات و فناوری - دانشگاه الزهراء - دانشکده علوم پایه 1391

در این پایان نامه رنگ آمیزی دینامیکی یک گراف را بیان و مطالعه می کنیم. یک –kرنگ آمیزی سره ی رأسی گراف g را رنگ آمیزی دینامیکی می نامند اگر در همسایه های هر رأس v?v(g) با درجه ی حداقل 2، حداقل 2 رنگ متفاوت ظاهر شوند. کوچکترین عدد صحیح k، به طوری که g دارای –kرنگ آمیزی دینامیکی باشد را عدد رنگی دینامیکی g می نامند و آنرا با نماد ?_2 (g) نمایش می دهند. مونت گمری حدس زده است که تمام گراف های منتظم ...

Journal: :Linear Algebra and its Applications 2022

A mixed graph is called second kind hermitian integral (or HS-integral) if the eigenvalues of its Hermitian-adjacency matrix are integers. Eisenstein (0, 1)-adjacency Let ? be an abelian group. We characterize set S for which a Cayley Cay(?,S) HS-integral. also show that and only it

Journal: :CoRR 2015
Oliver Knill

The spectrum of the Laplacian of successive Barycentric subdivisions of a graph converges exponentially fast to a limit which only depends on the clique number of the initial graph and not on the graph itself. Announced in [40]), the proof uses now an explicit linear operator mapping the clique vector of a graph to the clique vector of the Barycentric refinement. The eigenvectors of its transpo...

Journal: :Indagationes Mathematicae 2023

There are many research available on the study of a real-valued fractal interpolation function and dimension its graph. In this paper, our main focus is to dimensional results for vector-valued Riemann–Liouville fractional integral. Here, we give some which ensure that functions quite different from functions. We determine interesting bounds Hausdorff graph function. also obtain associated inva...

2016
ZUOQIANG SHI WEI ZHU

Abstract. Inspired by the graph Laplacian and the point integral method, we introduce a novel weighted graph Laplacian method to compute a smooth interpolation function on a point cloud in high dimensional space. The numerical results in semi-supervised learning and image inpainting show that the weighted graph Laplacian is a reliable and efficient interpolation method. In addition, it is easy ...

Journal: :Linear Algebra and its Applications 2023

A mixed graph is said to be second kind hermitian integral (HS-integral) if the eigenvalues of its Hermitian-adjacency matrix are integers. called Eisenstein (0, 1)-adjacency We characterize set S for which normal Cayley Cay(Γ,S) HS-integral any finite group Γ. further show that a and only it integral. This paper generalizes results Kadyan Bhattacharjy (2022) [11].

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