Results 31 to 40 of about 1,906 (145)
Planar, Outerplanar, and Toroidal Graphs of the Generalized Zero‐Divisor Graph of Commutative Rings
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 Let A be a commutative ring with unity and let set of all zero divisors of A be denoted by ZA. An ideal ℐ of the ring A is said to be essential if it has a nonzero intersection with every nonzero ideal of A. It is denoted by ℐ≤eA. The generalized zero‐divisor graph denoted by ΓgA is an undirected graph with vertex set ZA∗ (set of all nonzero zero ...
Abdulaziz M. Alanazi +3 more
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Lict edge semientire graph of a planar graph. [PDF]
, 2007 In this paper, we introduce the concept of the Lict edge semientire graph of a planar graph. We present characterizations of graphs whose lict edge semientire graphs are planar, outerplanar and Maximal outerplanar, crossing number one.
Maralabhavi, Y.B., Venkanagouda, M.G.
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On pathos lict graph of a tree [PDF]
, 2003 In this paper, the concept of pathos lict graph of a tree is introduced. We present a characterization of those graphs whose pathos lict graphs are planar, outerplanar, maximal outerplanar, crossing number one, eulerian and ...
Chandrasekhar, R., Muddebihal, M.H.
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The total chord length of maximal outerplanar graphs [PDF]
We consider embeddings of maximal outerplanar graphs whose vertices all lie on a cycle $\mathcal{C}$ bounding a face. Each edge of the graph that is not in $\mathcal{C}$, a chord, is assigned a length equal to the length of the shortest path in $\mathcal{C}$ between its endpoints. We define the total chord length of a graph as the sum of lengths of all
Haley Broadus, Elena Pavelescu
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Space-Efficient Biconnected Components and Recognition of Outerplanar Graphs [PDF]
, 2016 We present space-efficient algorithms for computing cut vertices in a given graph with $n$ vertices and $m$ edges in linear time using $O(n+\min\{m,n\log \log n\})$ bits.
Kammer, Frank +2 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
doaj +1 more source
Total domination in maximal outerplanar graphs II
Discrete Mathematics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dorfling, Michael +2 more
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A Note on Edge‐Group Choosability of Planar Graphs without 5‐Cycles
Journal of Mathematics, Volume 2020, Issue 1, 2020., 2020 This paper is devoted to a study of the concept of edge‐group choosability of graphs. We say that G is edge‐k‐group choosable if its line graph is k‐group choosable. In this paper, we study an edge‐group choosability version of Vizing conjecture for planar graphs without 5‐cycles and for planar graphs without noninduced 5‐cycles (2010 Mathematics ...
Amir Khamseh, Andrei V. Kelarev
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Nonplanarity of Iterated Line Graphs
Journal of Mathematics, Volume 2020, Issue 1, 2020., 2020 The 1‐crossing index of a graph G is the smallest integer k such that the kth iterated line graph of G has crossing number greater than 1. In this paper, we show that the 1‐crossing index of a graph is either infinite or it is at most 5. Moreover, we give a full characterization of all graphs with respect to their 1‐crossing index.
Jing Wang, Alfred Peris
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Game Chromatic Number of Generalized Petersen Graphs and Jahangir Graphs
Journal of Applied Mathematics, Volume 2020, Issue 1, 2020., 2020 Let G = (V, E) be a graph, and two players Alice and Bob alternate turns coloring the vertices of the graph G a proper coloring where no two adjacent vertices are signed with the same color. Alice′s goal is to color the set of vertices using the minimum number of colors, which is called game chromatic number and is denoted by χg(G), while Bob′s goal is
Ramy Shaheen +3 more
wiley +1 more source