Results 11 to 20 of about 1,844,339 (310)
Discrete Mathematics, 2011 Boxicity of a graph H, denoted by box(H), is the minimum integer k such that H is an intersection graph of axis-parallel k-dimensional boxes in R^k. In this paper, we show that for a line graph G of a multigraph, box(G) <= 2 (\lceil log_2(log_2( )) \rceil + 3) + 1, where denotes the maximum degree of G. Since <= 2( - 1), for any line graph
Chandran, Sunil L +2 more
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An Even 2-Factor in the Line Graph of a Cubic Graph
Theory and Applications of Graphs, 2022 An even 2-factor is one such that each cycle is of even length. A 4- regular graph G is 4-edge-colorable if and only if G has two edge-disjoint even 2- factors whose union contains all edges in G.
SeungJae Eom, Kenta Ozeki
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Omega Index of Line and Total Graphs
Journal of Mathematics, 2021 A derived graph is a graph obtained from a given graph according to some predetermined rules. Two of the most frequently used derived graphs are the line graph and the total graph.
Musa Demirci +3 more
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A number theoretic problem on super line graphs
AKCE International Journal of Graphs and Combinatorics, 2016 In Bagga et al. (1995) a generalization of the line graph concept was introduced. Given a graph G with at least r edges, the super line graph of index r, Lr(G), has as its vertices the sets of r edges of G, with two adjacent if there is an edge in one ...
Jay Bagga, Lowell Beineke, Badri Varma
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Outerplanarity of line graphs and iterated line graphs
Applied Mathematics Letters, 2011 AbstractThe outerplanar index of a graph G is the smallest integer k such that the kth iterated line graph of G is non-outerplanar. In this note, we show: (i) the characterization of the forbidden subgraphs for graphs with outerplanar line graphs; (ii) that the outerplanar index of a graph is either infinite or at most 3.
Huiqiu Lin +4 more
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On the application of line graphs in quantitative structure-property studies [PDF]
Journal of the Serbian Chemical Society, 2000 Let G be a molecular graph possessing m0(G) edges. Let m1(G) be the number of edges of the line graph L(G) of G, known as the Bertz index. Let m2(G) be the number of edges of the line graph of L(G), etc.
Gutman Ivan, Tomović Željko
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Graphs whose line graphs are ring graphs
AKCE International Journal of Graphs and Combinatorics, 2020 Given a graph H, a path of length at least two is called an H-path if meets H exactly in its ends. A graph G is a ring graph if each block of G which is not a bridge or a vertex can be constructed inductively by starting from a single cycle and then in ...
Mahdi Reza Khorsandi
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On the Planarity of Generalized Line Graphs
Theory and Applications of Graphs, 2019 One of the most familiar derived graphs is the line graph. The line graph $L(G)$ of a graph $G$ is that graph whose vertices are the edges of $G$ where two vertices of $L(G)$ are adjacent if the corresponding edges are adjacent in~$G$.
Khawlah H. Alhulwah +2 more
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General Randić indices of a graph and its line graph
Open Mathematics, 2023 For a real number α\alpha , the general Randić index of a graph GG, denoted by Rα(G){R}_{\alpha }\left(G), is defined as the sum of (d(u)d(v))α{\left(d\left(u)d\left(v))}^{\alpha } for all edges uvuv of GG, where d(u)d\left(u) denotes the degree of a ...
Liang Yan, Wu Baoyindureng
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The H-Line Signed Graph of a Signed Graph [PDF]
, 2010 For standard terminology and notion in graph theory we refer the reader to Harary; the non-standard will be given in this paper as and when required.
Rangarajan, R. +2 more
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