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Jambura Journal of Mathematics, 2022 Let G = (V(G), E(G)) be a connected graph, where V(G) is the set of vertices and E(G) is the set of edges. The set Dt(G) is called the total domination set in G if every vertex v 2 V(G) is adjacent to at least one vertex in Dt (G).
Nurhamzah Nurhamzah +2 more
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Exact Formula and Improved Bounds for General Sum-Connectivity Index of Graph-Operations
IEEE Access, 2019 For a molecular graph Γ, the general sum-connectivity index is defined as χβ(Γ) = Σvw∈E(Γ)[dΓ(v) + dΓ(w)]β, where β ∈ R and dΓ(v) denotes the degree of the vertex ...
Maqsood Ahmad +3 more
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New results of partially total fuzzy graph
BMC Research Notes, 2023 Objective The study of total fuzzy graphs in all cases is crucial for the development of both theories and applications of the graph theory. Without theory the application will not be developed.
Fekadu Tesgera Agama +2 more
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Total Weight Choosability of Graphs [PDF]
The Electronic Journal of Combinatorics, 2011 Suppose the edges and the vertices of a simple graph $G$ are assigned $k$-element lists of real weights. By choosing a representative of each list, we specify a vertex colouring, where for each vertex its colour is defined as the sum of the weights of its incident edges and the weight of the vertex itself.
Przybyło, Jakub, Woźniak, Mariusz
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Blind Image Deblurring via Reweighted Graph Total Variation
, 2017 Blind image deblurring, i.e., deblurring without knowledge of the blur kernel, is a highly ill-posed problem. The problem can be solved in two parts: i) estimate a blur kernel from the blurry image, and ii) given estimated blur kernel, de-convolve blurry
Bai, Yuanchao +3 more
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The sharp bounds on general sum-connectivity index of four operations on graphs
Journal of Inequalities and Applications, 2016 The general sum-connectivity index χ α ( G ) $\chi_{\alpha}(G)$ , for a (molecular) graph G, is defined as the sum of the weights ( d G ( a 1 ) + d G ( a 2 ) ) α $(d_{G}(a_{1})+d_{G}(a_{2}))^{\alpha}$ of all a 1 a 2 ∈ E ( G ) $a_{1}a_{2}\in E(G)$ , where
Shehnaz Akhter, Muhammad Imran
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Computing Metric Dimension of Power of Total Graph
IEEE Access, 2021 For a connected graph $\mathcal {G}$ , the distance $d(u, v)$ between any two vertices $u$ , $v~\in ~\mathcal {V(G)}$ is defined as; $d(u,v)=\min _{\mathcal {P}_{u,v}}\{\text {length of}~\mathcal {P}_{uv}\}$ i.e the minimum length of path ...
Sehar Nawaz +3 more
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Total coloring of 1-toroidal graphs of maximum degree at least 11 and no adjacent triangles
, 2018 A {\em total coloring} of a graph $G$ is an assignment of colors to the vertices and the edges of $G$ such that every pair of adjacent/incident elements receive distinct colors.
AV Kostochka +16 more
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Isolation Number of Transition Graphs
MathematicsLet G=(V,E) be a graph and F be a family of graphs; a subset (S⊆V(G)) is said to be an F-isolating set if G[V(G)∖NG[S]] does not contain F as a subgraph for all F∈F.
Junhao Qu, Shumin Zhang
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Genus of total graphs from rings: A survey
AKCE International Journal of Graphs and Combinatorics, 2018 Let be a commutative ring. The total graph of is the undirected graph with vertex set and two distinct vertices and are adjacent if is a zero divisor in In this paper, we present a survey of results on the genus of and three of its generalizations.
T. Tamizh Chelvam, T. Asir
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