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Graphs whose line graphs are ring graphs [PDF]
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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Line graphs of directed graphs I [PDF]
Transactions on CombinatoricsWe determine the forbidden induced subgraphs for the intersection of the classes of chordal bipartite graphs and line graphs of acyclic directed graphs. This is a first step towards finding the forbidden induced subgraphs for the class of line graphs of ...
Vaidyanathan Sivaraman, Daniel Slilaty
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Neutrosophic Vague Line Graphs [PDF]
Neutrosophic Sets and Systems, 2020 Neutrosophic graphs are employed as a mathematical key to hold an imprecise and unspecified data. Vague sets gives more intuitive graphical notation of vague information, that delicates crucially better analysis in data relationships, incompleteness and ...
S. Satham Hussain +2 more
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A preservice middle school mathematics teacher’s knowledge of student thinking about line graphs [PDF]
Journal of Pedagogical Research, 2022 Interpreting statistical graphs and making inferences based on the graphs are a precursor for formal statistical inferences. To support student inferences, both teachers and future teachers should have adequate knowledge regarding students’ thinking on ...
Aytug Ozaltun Celik
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Line Graphs of Monogenic Semigroup Graphs
Journal of Mathematics, 2021 The concept of monogenic semigroup graphs ΓSM is firstly introduced by Das et al. (2013) based on zero divisor graphs. In this study, we mainly discuss the some graph properties over the line graph LΓSM of ΓSM.
Nihat Akgunes +2 more
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Sombor Index Under Some Graph Products [PDF]
Mathematics Interdisciplinary Research, 2022 Let G=(V, E) be a graph with vertex set V(G) and edge set E(G). The Sombor index of a graph G, SO(G), is defined as ∑uv∈ E(G) √(d2u+d2v), where du is the degree of vertex u in V(G). In the present paper, we determine the lower bound for the
Irandokht Rezaee Abdolhosseinzadeh +2 more
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On chordal graph and line graph squares [PDF]
Discrete Applied Mathematics, 2018 In this work we investigate the chordality of squares and line graph squares of graphs. We prove a sufficient condition for the chordality of squares of graphs not containing induced cycles of length at least five. Moreover, we characterize the chordality of graph squares by forbidden subgraphs.
Robert Scheidweiler +1 more
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Treewidth of the Line Graph of a Complete Graph [PDF]
Journal of Graph Theory, 2014 AbstractIn recent articles by Grohe and Marx, the treewidth of the line graph of a complete graph is a critical example—in a certain sense, every graph with large treewidth “contains” . However, the treewidth of was not determined exactly. We determine the exact treewidth of the line graph of a complete graph.
Daniel J. Harvey, David R. Wood
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Bounds on the connectivity of iterated line graphs
Electronic Journal of Graph Theory and Applications, 2022 For simple connected graphs that are neither paths nor cycles, we define l(G)=max{m : G has a divalent path of length m that is not both of length 2 and in a K3}, where a divalent path is a path whose internal vertices have degree two in G.
Yehong Shao
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Axioms, 2022 The Randić index of a graph G, denoted by R(G), is defined as the sum of 1/d(u)d(v) for all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this note, we show that R(L(T))>n4 for any tree T of order n≥3.
Jiangfu Zhang, Baoyindureng Wu
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