Results 31 to 40 of about 180 (113)
Detour index of a class of unicyclic graphs
, 2010 The detour index of a connected graph is defined as the sum of detour distances between all unordered pairs of vertices. We determine the n-vertex unicyclic graphs whose vertices on its unique cycle all have degree at least three with the first, the ...
Qi Xuli, Bo Zhou
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A Characterization for 2-Self-Centered Graphs
Discussiones Mathematicae Graph Theory, 2018 A graph is called 2-self-centered if its diameter and radius both equal to 2. In this paper, we begin characterizing these graphs by characterizing edge-maximal 2-self-centered graphs via their complements.
Shekarriz Mohammad Hadi +2 more
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Bounds on F-index of tricyclic graphs with fixed pendant vertices
Open Mathematics, 2020 The F-index F(G) of a graph G is obtained by the sum of cubes of the degrees of all the vertices in G. It is defined in the same paper of 1972 where the first and second Zagreb indices are introduced to study the structure-dependency of total π-electron ...
Akram Sana +2 more
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On Antipodal and Diametrical Partial Cubes
Discussiones Mathematicae Graph Theory, 2021 We prove that any diametrical partial cube of diameter at most 6 is antipodal. Because any antipodal graph is harmonic, this gives a partial answer to a question of Fukuda and Handa [Antipodal graphs and oriented matroids, Discrete Math.
Polat Norbert
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Resolving Edge Colorings: Exact Results and a Tabu Search Heuristic
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.This study presents new results on resolving edge colorings in graphs, a concept introduced by V. Saenpholphat and P. Zhang in 2003. We determine the resolving edge chromatic number for several well‐known families of graphs, including complete graphs, complete bipartite graphs, wheel graphs, sun graphs, and friendship graphs.
Narjes Sabeghi +4 more
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The Second Neighbourhood for Bipartite Tournaments
Discussiones Mathematicae Graph Theory, 2019 Let T (X ∪ Y, A) be a bipartite tournament with partite sets X, Y and arc set A. For any vertex x ∈ X ∪Y, the second out-neighbourhood N++(x) of x is the set of all vertices with distance 2 from x.
Li Ruijuan, Sheng Bin
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Independence Number and Packing Coloring of Generalized Mycielski Graphs
Discussiones Mathematicae Graph Theory, 2021 For a positive integer k ⩾ 1, a graph G with vertex set V is said to be k-packing colorable if there exists a mapping f : V ↦ {1, 2, . . ., k} such that any two distinct vertices x and y with the same color f(x) = f(y) are at distance at least f(x) + 1 ...
Bidine Ez Zobair +2 more
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An Exact Determination of the Radio Number of Graph Hn for n ≥ 15
Journal of Mathematics, Volume 2026, Issue 1, 2026.Suppose that G is a connected graph. For any two vertices u and v, let dG (u,v) denote the distance between u and v in G. The diameter of G is the maximum distance between any pair of vertices, and it is denoted by diam(G). A multilevel distance labeling (or radio condition) for G is a function f that assigns to each vertex of G a positive integer such
Munawwar Hussain +5 more
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Journal of Mathematics, Volume 2026, Issue 1, 2026.Let G be a connected graph. A subset S⊆V(G) is called a general position set of a graph G if no shortest path in G contains more than two vertices from S. Likewise, a subset X⊆E(G) is an edge general position set if no shortest path contains more than two edges from X.
Zahra Hamed-Labbafian +2 more
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Dualizing Distance-Hereditary Graphs
Discussiones Mathematicae Graph Theory, 2021 Distance-hereditary graphs can be characterized by every cycle of length at least 5 having crossing chords. This makes distance-hereditary graphs susceptible to dualizing, using the common extension of geometric face/vertex planar graph duality to cycle ...
McKee Terry A.
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