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Under which conditions is λ″(G)=κ″(L(G))?
AKCE International Journal of Graphs and Combinatorics, 2023 In this paper we show that if G is a connected graph such that [Formula: see text], [Formula: see text] and [Formula: see text] then [Formula: see text] exists and [Formula: see text] if and only if G is not super-[Formula: see text]. We also obtain some
Farnaz Soliemany +2 more
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The Line n-Sigraph of a Symmetric n-Sigraph-IV [PDF]
, 2012 Unless mentioned or defined otherwise, for all terminology and notion in graph theory the reader is refer to [6].
Reddy, P. Siva Kota +5 more
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On the planarity of line Mycielskian graph of a graph
Ratio Mathematica, 2020 The line Mycielskian graph of a graph G, denoted by Lμ(G) is defined as the graph obtained from L(G) by adding q+1 new vertices E' = ei' : 1 ≤ i ≤ q and e, then for 1 ≤ i ≤ q , joining ei' to the neighbours of ei and to e.
Keerthi G. Mirajkar +1 more
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AKCE International Journal of Graphs and Combinatorics, 2021 Let be a graph. A local edge coloring of G is a proper edge coloring such that for each subset S of E(G) with there exist edges such that where ns is the number of copies of P3 in the edge induced subgraph The maximum color assigned by a local edge ...
P. Deepa +2 more
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Resolving sets of vertices with the minimum size in graphs [PDF]
ریاضی و جامعه, 2023 Suppose that $G$ is a simple connected graph with vertex set $V(G)$ and edge set $E(G)$. A subset $S=\{s_1, s_2,\ldots , s_l \}$ of vertices of graph $G$ is called a doubly resolving set of $G$, if for any distinct vertices $u$ and $v$ in $G$ there are ...
Ali Zafari, Nader Habibi, Saeid Alikhani
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On an edge partition and root graphs of some classes of line graphs
Electronic Journal of Graph Theory and Applications, 2017 The Gallai and the anti-Gallai graphs of a graph $G$ are complementary pairs of spanning subgraphs of the line graph of $G$. In this paper we find some structural relations between these graph classes by finding a partition of the edge set of the line ...
K Pravas, A. Vijayakumar
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Construction and analysis of graph models for multiprocessor interconnection networks [PDF]
Yugoslav Journal of Operations Research, 2022 A graph G can serve as a model for the Multiprocessor Interconnection Networks (MINs) in which the vertices represent the processors, while the edges represent connections between processors.
Hegde S.M., Saumya Y.M.
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Complex, 2020 Let G be a finite, connected graph of order of, at least, 2 with vertex set VG and edge set EG. A set S of vertices of the graph G is a doubly resolving set for G if every two distinct vertices of G are doubly resolved by some two vertices of S.
Jia-bao Liu, A. Zafari
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On Pathos Total Semitotal and Entire Total Block Graph of a Tree [PDF]
, 2012 In this communication, the concept of pathos total semitotal and entire total block graph of a tree is introduced. Its study is concentrated only on trees.
Syed Babajan +2 more
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Discussiones Mathematicae Graph Theory, 2013 The infimum of the least eigenvalues of all finite induced subgraphs of an infinite graph is defined to be its least eigenvalue. In [P.J. Cameron, J.M. Goethals, J.J. Seidel and E.E. Shult, Line graphs, root systems, and elliptic geometry, J. Algebra 43 (
Vijayakumar Gurusamy Rengasamy
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