Results 11 to 20 of about 2,253,480 (276)
Total Graphs and Traversability [PDF]
Proceedings of the Edinburgh Mathematical Society, 1966 With every graph G (finite and undirected with no loops or multiple lines) there is associated a graph L(G), called the line-graph of G, whose points correspond in a one-to-one manner with the lines of G in such a way that two points of L(G) are adjacent if and only if the corresponding lines of Gare adjacent. This concept was originated by Whitney (3).
Behzad, Mehdi, Chartrand, Gary
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On the Total Set Chromatic Number of Graphs
Theory and Applications of Graphs, 2022 Given a vertex coloring c of a graph, the neighborhood color set of a vertex is defined to be the set of all of its neighbors’ colors. The coloring c is called a set coloring if any two adjacent vertices have different neighborhood color sets.
Mark Anthony C. Tolentino +2 more
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On two energy-like invariants of line graphs and related graph operations
Journal of Inequalities and Applications, 2016 For a simple graph G of order n, let μ 1 ≥ μ 2 ≥ ⋯ ≥ μ n = 0 $\mu_{1}\geq\mu_{2}\geq\cdots\geq\mu_{n}=0$ be its Laplacian eigenvalues, and let q 1 ≥ q 2 ≥ ⋯ ≥ q n ≥ 0 $q_{1}\geq q_{2}\geq\cdots\geq q_{n}\geq0$ be its signless Laplacian eigenvalues.
Xiaodan Chen, Yaoping Hou, Jingjian Li
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Wiener index of graphs over rings: a survey
AKCE International Journal of Graphs and Combinatorics, 2022 This article presents a survey of results consisting of the Wiener index of graphs associated with commutative rings. In particular, we focus on zero-divisor graphs, unit graphs, total graphs and prime graphs.
T. Asir +3 more
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Graph equations for line graphs, total graphs, middle graphs and quasi-total graphs
Discrete Mathematics, 1984 Let G be a simple finite and connected graph with the vertex set V(G) and the edge set X(G). Let V'(G) be the family of all one-point subsets of V(G). Both the line graph L(G) of G and the total graph T(G) of G are standard graph theoretical concepts. The middle graph M(G) of G is the intersection graph of \(V'(G)\cup X(G)\) and the quasi-total graph P(
Sastry, D.V.S, Raju, B.Syam Prasad
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Total Minimal Dominating Signed Graph [PDF]
, 2010 Cartwright and Harary considered graphs in which vertices represent persons and the edges represent symmetric dyadic relations amongst persons each of which designated as being positive or negative according to whether the nature of the relationship is ...
Reddy, Siva Kota, Vijay, S.
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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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Augmenting graphs to minimize the diameter [PDF]
, 2013 We study the problem of augmenting a weighted graph by inserting edges of bounded total cost while minimizing the diameter of the augmented graph.
A.A. Schoone +14 more
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On the Total Graph of Mycielski Graphs, Central Graphs and Their Covering Numbers
Discussiones Mathematicae Graph Theory, 2013 The technique of counting cliques in networks is a natural problem. In this paper, we develop certain results on counting of triangles for the total graph of the Mycielski graph or central graph of star as well as completegraph families.
Patil H.P., Pandiya Raj R.
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An efficient and fair solution for communication graph games\ud [PDF]
, 2011 We introduce an efficient solution for games with communication graph structures and show that it is characterized by efficiency, fairness and a new axiom called component balancedness.
Anna Khmelnitskaya +6 more
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