Results 31 to 40 of about 1,119 (103)
Spectra of Orders for k-Regular Graphs of Girth g
Discussiones Mathematicae Graph Theory, 2021 A (k, g)-graph is a k-regular graph of girth g. Given k ≥ 2 and g ≥ 3, infinitely many (k, g)-graphs of infinitely many orders are known to exist. Our goal, for given k and g, is the classification of all orders n for which a (k, g)-graph of order n ...
Jajcay Robert, Raiman Tom
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Closed and asymptotic formulas for energy of some circulant graphs
, 2016 We consider circulant graphs G(r,N) where the vertices are the integers modulo N and the neighbours of 0 are {-r,...,-1,1,...,r}. The energy of G(r,N) is a trigonometric sum of N*r terms. For low values of r we compute this sum explicitly.
Arango, Carlos Alberto Marín +1 more
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Journal of Mathematics, Volume 2025, Issue 1, 2025.In its crystalline state, the α‐icosahedral nanosheet of boron demonstrates superconductivity and thermal electronic properties. Mathematical research on a graph’s structure yields a graph descriptor, a numerical measure. Chemical graph theory employs connectivity descriptors to analyze molecular structures, providing crucial insights into many ...
Khalil Hadi Hakami +3 more
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Gaps in the Saturation Spectrum of Trees
Discussiones Mathematicae Graph Theory, 2019 A graph G is H-saturated if H is not a subgraph of G but the addition of any edge from the complement of G to G results in a copy of H. The minimum number of edges (the size) of an H-saturated graph on n vertices is denoted sat(n,H), while the maximum ...
Horn Paul +3 more
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Spectral radius and traceability of connected claw-free graphs
, 2015 Let $G$ be a connected claw-free graph on $n$ vertices and $\overline{G}$ be its complement graph. Let $\mu(G)$ be the spectral radius of $G$. Denote by $N_{n-3,3}$ the graph consisting of $K_{n-3}$ and three disjoint pendent edges. In this note we prove
Li, Binlong, Ning, Bo
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The Degree-Diameter Problem for Outerplanar Graphs
Discussiones Mathematicae Graph Theory, 2017 For positive integers Δ and D we define nΔ,D to be the largest number of vertices in an outerplanar graph of given maximum degree Δ and diameter D. We prove that nΔ,D=ΔD2+O (ΔD2−1)$n_{\Delta ,D} = \Delta ^{{D \over 2}} + O\left( {\Delta ^{{D \over 2 ...
Dankelmann Peter +2 more
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Extremal Digraphs Avoiding Distinct Walks of Length 4 with the Same Endpoints
Discussiones Mathematicae Graph Theory, 2022 Let n ≥ 8 be an integer. We characterize the extremal digraphs of order n with the maximum number of arcs avoiding distinct walks of length 4 with the same endpoints.
Lyu Zhenhua
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Maximal Independent Sets In Graphs With At Most r Cycles
, 2005 We find the maximum number of maximal independent sets in two families of graphs: all graphs with $n$ vertices and at most $r$ cycles, and all such graphs that are also connected.
Diestel +9 more
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On the maximal Aa -index of graphs with a prescribed number of edges
Special MatricesFor any real number α∈[0,1]\alpha \in \left[\mathrm{0,1}], by the Aα{A}_{\alpha }-matrix of a graph GG, we mean the matrix Aα(G)=αD(G)+(1−α)A(G){A}_{\alpha }\left(G)=\alpha D\left(G)+\left(1-\alpha )A\left(G), where A(G)A\left(G) and D(G)D\left(G) are ...
Chang Ting-Chung, Tam Bit-Shun
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Hamiltonian and Pancyclic Graphs in the Class of Self-Centered Graphs with Radius Two
Discussiones Mathematicae Graph Theory, 2018 The paper deals with Hamiltonian and pancyclic graphs in the class of all self-centered graphs of radius 2. For both of the two considered classes of graphs we have done the following. For a given number n of vertices, we have found an upper bound of the
Hrnčiar Pavel, Monoszová Gabriela
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