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Extremal Values on the General Degree–Eccentricity Index of Unicyclic Graphs of Fixed Diameter
Journal of MathematicsFor a connected graph G and two real numbers a,b, the general degree–eccentricity index of G is given by DEIa,bG=∑v∈VGdGavecGbv, where VG represent the vertex set of graph G, dGv denotes the degree of vertex v, and ecGv is the eccentricity of v in G ...
Mesfin Masre
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Trees with Distinguishing Index Equal Distinguishing Number Plus One
Discussiones Mathematicae Graph Theory, 2020 The distinguishing number (index) D(G) (D′ (G)) of a graph G is the least integer d such that G has an vertex (edge) labeling with d labels that is preserved only by the trivial automorphism.
Alikhani Saeid +3 more
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The domination number and the least $Q$-eigenvalue [PDF]
, 2013 A vertex set $D$ of a graph $G$ is said to be a dominating set if every vertex of $V(G)\setminus D$ is adjacent to at least a vertex in $D$, and the domination number $\gamma(G)$ ($\gamma$, for short) is the minimum cardinality of all dominating sets of $
Guo, Shu-Guang +3 more
core
Degree distance of unicyclic graphs
Filomat, 2010 The degree distance of a connected graph G with vertex set V(G) is defined as D'(G)= ?u?V (G) dG (u)DG (u), where dG (u) denotes the degree of vertex u and DG (u) denotes the sum of distances between u and all vertices of G. We determine the maximum degree distance of n-vertex unicyclic graphs with given maximum degree, and the first seven maximum ...
Zhibin Du, Bo Zhou
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Resolving an Open Problem on the Exponential Arithmetic–Geometric Index of Unicyclic Graphs
MathematicsRecently, the exponential arithmetic–geometric index (EAG) was introduced. The exponential arithmetic–geometric index (EAG) of a graph G is defined as EAG(G)=∑vivj∈E(G)edi+dj2didj, where di represents the degree of the vertex vi in G.
Kinkar Chandra Das, Jayanta Bera
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Locating eigenvalues of unicyclic graphs
Applicable Analysis and Discrete Mathematics, 2017 We present a linear time algorithm that computes the number of eigenvalues of a unicyclic graph in a given real interval. It operates directly on the graph, so that the matrix is not needed explicitly. The algorithm is applied to study the multiplicities of eigenvalues of closed caterpillars, obtain the spectrum of balanced closed ...
Braga, Rodrigo O. +2 more
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The Neighbor-Locating-Chromatic Number of Pseudotrees
, 2020 A $k$-coloring of a graph $G$ is a partition of the set of vertices of $G$ into $k$ independent sets, which are called colors. A $k$-coloring is neighbor-locating if any two vertices belonging to the same color can be distinguished from each other by the
Alcon, Liliana +4 more
core
Restrained domination in unicyclic graphs
Discussiones Mathematicae Graph Theory, 2009 Let G = (V,E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex in V − S is adjacent to a vertex in S and to a vertex in V − S. The restrained domination number of G, denoted by γr(G), is the minimum cardinality of a restrained dominating set of G. A unicyclic graph is a connected graph that contains precisely one cycle.
Johannes H. Hattingh +4 more
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Zagreb Indices of Trees, Unicyclic and Bicyclic Graphs With Given (Total) Domination
IEEE Access, 2019 Let G = (V, E) be a (molecular) graph. For a family of graphs G, the first Zagreb index M1 and the second Zagreb index M2 have already studied. In particular, it has been presented, the first Zagreb index M1 and the second Zagreb index M2 of trees T in ...
Doost Ali Mojdeh +3 more
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Spectrum of Unicyclic Graph [PDF]
Advances in Computer Science Research, 2022 Agung Lukito +3 more
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