Results 41 to 50 of about 580,793 (206)
Smarandachely t-path step signed graphs [PDF]
, 2010 Characterizing signed graphs which are switching equivalent to their Smarandachely 3-path step signed ...
Reddy, Siva Kota +5 more
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Identifying the Exact Value of the Metric Dimension and Edge Dimension of Unicyclic Graphs
Mathematics, 2022 Given a simple connected graph G, the metric dimension dim(G) (and edge metric dimension edim(G)) is defined as the cardinality of a smallest vertex subset S⊆V(G) for which every two distinct vertices (and edges) in G have distinct distances to a vertex ...
Enqiang Zhu +2 more
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On The Packing k-Coloring of Unicyclic Graph Family [PDF]
, 2020 All graph in this paper is connected graph. Let du,v be a distance between any vertex u and v in graph GV,E. A function c :VG 1, 2, , k is called a packing k coloring if every two vertex of color i are at least distance i 1.
KRISTIANA, Arika Indah +2 more
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On unicyclic graphs of metric dimension 2 [PDF]
, 2017 A metric basis S of a graph G is the subset of vertices of minimum cardinality such that all other vertices are uniquely determined by their distances to the vertices in S. The metric dimension of a graph G is the cardinality of the subset S.
Dudenko, M., Oliynyk, B.
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Some Results on the Independence Polynomial of Unicyclic Graphs
Discussiones Mathematicae Graph Theory, 2018 Let G be a simple graph on n vertices. An independent set in a graph is a set of pairwise non-adjacent vertices. The independence polynomial of G is the polynomial I(G,x)=∑k=0ns(G,k)xk$I(G,x) = \sum\nolimits_{k = 0}^n {s\left({G,k} \right)x^k }$, where s(
Oboudi Mohammad Reza
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Edge colouring line graphs of unicyclic graphs
Discrete Applied Mathematics, 1992 A characterization of line graphs of unicyclic graphs is established, and it is proved that the line graph \(G\) of a unicyclic graph is in class 1 unless \(G\) is an odd cycle and an optimal edge colouring of the line graph of a unicyclic graph can be computed in time \(O(| E|)\) (note that the chromatic index problem is known to be \(NP\)-complete ...
Leizhen Cai, John A. Ellis
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On Unicyclic Graphs Spectra: New Results
2016 IEEE Intl Conference on Computational Science and Engineering (CSE) and IEEE Intl Conference on Embedded and Ubiquitous Computing (EUC) and 15th Intl Symposium on Distributed Computing and Applications for Business Engineering (DCABES), 2016 Let G = (V, E) be a unicyclic simple undirected graph. In this paper, we investigate the spectra of a particular class of unicyclic graphs G(q, n1) where q is the size of the unique cycle. Each vertex of the unique cycle is attached to n1 vertices. We provide the " exact values " of the extremal eigenvalues of the adjacency matrix A and the Laplacian ...
Hadji, Makhlouf, Chau, Ming
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AKCE International Journal of Graphs and Combinatorics, 2023 For a connected simple graph G, the inverse degree index and forgotten index are defined as [Formula: see text] and [Formula: see text] respectively, where [Formula: see text] denotes the degree of vertex u in G.
Mohammad Ali Manian +2 more
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On Minimum Wiener Polarity Index of Unicyclic Graphs with Prescribed Maximum Degree
Journal of Applied Mathematics, 2014 The Wiener polarity index of a connected graph G is defined as the number of its pairs of vertices that are at distance three. By introducing some graph transformations, in different way with that of Huang et al., 2013, we determine the minimum Wiener ...
Jianping Ou, Xing Feng, Saihua Liu
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A survey and a new class of graceful unicylic graphs
AKCE International Journal of Graphs and Combinatorics, 2020 A graph G admits a graceful labeling if there is a one-to-one map f from the set of vertices of G to such that when an edge xy is assigned the label the resulting set of edge labels is When such a labeling exists, G is called graceful. Rosa showed that a
Max Pambe Biatch’ +2 more
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