Results 41 to 50 of about 1,202 (110)
The upper bounds for multiplicative sum Zagreb index of some graph operations
, 2017 Let G be a simple graph with vertex set V(G) and edge set E(G). In [7], Eliasi et al. introduced the multiplicative sum Zagreb index of a graph G which is denoted by Π1(G) and is defined by Π1(G) = ∏ uv∈V (G) (dG(u)+dG(v)) .
Yasar Nacaroglu, A. D. Maden
semanticscholar +1 more source
Exact solutions to the Erdős-Rothschild problem
Forum of Mathematics, SigmaLet $\boldsymbol {k} := (k_1,\ldots ,k_s)$ be a sequence of natural numbers. For a graph G, let $F(G;\boldsymbol {k})$ denote the number of colourings of the edges of G with colours $1,\dots ,s$ such that, for every $c \in \{1 ...
Oleg Pikhurko, Katherine Staden
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On extremal numbers of the triangle plus the four-cycle
Forum of Mathematics, SigmaFor a family $\mathcal {F}$ of graphs, let ${\mathrm {ex}}(n,\mathcal {F})$ denote the maximum number of edges in an n-vertex graph which contains none of the members of $\mathcal {F}$ as a subgraph.
Jie Ma, Tianchi Yang
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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
core +1 more source
The harmonic index for unicyclic and bicyclic graphs with given matching number
, 2015 The harmonic index of a graph G is defined as the sum of the weights 2 d.u/Cd.v/ of all edges uv of G, where d.u/ denotes the degree of a vertex u in G.
Lingping Zhong
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On the cycle structure of hamiltonian k-regular bipartite graphs of order 4k [PDF]
, 2009 It is shown that a hamiltonian $n/2$-regular bipartite graph $G$ of order $2n>8$ contains a cycle of length $2n-2$. Moreover, if such a cycle can be chosen to omit a pair of adjacent vertices, then $G$ is bipancyclic.Comment: 3 ...
Adamus, Janusz
core
Extermal properties of Zagreb coindices and degree distance of graphs
, 2010 The degree distance, Zagreb coindices and reverse degree distance of a connected graph have been studied in mathematical chemistry. In this paper some new extremal values of these topological invariants over some special classes of graphs are determined.
S. Hossein-Zadeh, A. Hamzeh, A. Ashrafi
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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
wiley +1 more source
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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