Results 41 to 50 of about 238 (93)
COMPUTING SANSKRUTI INDEX OF CAPRA-DESIGNED PLANAR BENZENOID SERIES $Ca_k(C_6)$
, 2017 Let G = (V,E) be a molecular graph, such that vertices represent atoms and edges are chemical bonds. The Sanskruti index of a graph G is a topological index was defined as S(G) = ∑ uv∈E(G)( SuSv Su+Sv−2 ) where Su is the summation of degrees of all ...
X. Zhang +4 more
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Total Resolving Number of Block Graphs and Line Graphs
, 2018 Let G = (V , E) be a simple connected graph. An ordered subset W of V is said to be a resolving set of G if every vertex is uniquely determined by its vector of distances to the vertices in W.
J. Joseph, N. Shunmugapriya
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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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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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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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Avoiding rainbow 2-connected subgraphs
Open Mathematics, 2017 While defining the anti-Ramsey number Erdős, Simonovits and Sós mentioned that the extremal colorings may not be unique. In the paper we discuss the uniqueness of the colorings, generalize the idea of their construction and show how to use it to ...
Gorgol Izolda
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More on the Rainbow Disconnection in Graphs
Discussiones Mathematicae Graph Theory, 2022 Let G be a nontrivial edge-colored connected graph. An edge-cut R of G is called a rainbow-cut if no two of its edges are colored the same. An edge-colored graph G is rainbow disconnected if for every two vertices u and v of G, there exists a u-v-rainbow-
Bai Xuqing +3 more
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Rainbow spanning structures in graph and hypergraph systems
Forum of Mathematics, Sigma, 2023 We study the following rainbow version of subgraph containment problems in a family of (hyper)graphs, which generalizes the classical subgraph containment problems in a single host graph. For a collection $\mathit {\mathbf {G}}=\{G_1, G_2,\ldots , G_{
Yangyang Cheng +3 more
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