Results 11 to 20 of about 2,615 (201)
Root square mean labelling of some graphs obtained from path
Journal of Physics: Conference Series, 2021 Abstract Let G be a graph with q edges. A labelling f of G is said to be root square mean labelling if f: V(G)UE(G)→{1,2,…,q+1} such that when each edge e = uv labelled with f(e)=[f(u)2+f(v)2/2] or f(e)=[f(u)2+f(v)2/2] then the resulting edge labels are distinct. A graph G is called a root square mean graph if G can be labelled by a root
R Ramdani +3 more
openaire +1 more source
Maximum Multiplicity of Matching Polynomial Roots and Minimum Path Cover in General Graphs [PDF]
The Electronic Journal of Combinatorics, 2011 Let $G$ be a graph. It is well known that the maximum multiplicity of a root of the matching polynomial $\mu(G,x)$ is at most the minimum number of vertex disjoint paths needed to cover the vertex set of $G$. Recently, a necessary and sufficient condition for which this bound is tight was found for trees.
Ku, C.Y., Wong, K.B.
openaire +2 more sources
Enumeration of N-rooted maps using quantum field theory
Nuclear Physics B, 2018 A one-to-one correspondence is proved between the N-rooted ribbon graphs, or maps, with e edges and the (e−N+1)-loop Feynman diagrams of a certain quantum field theory.
K. Gopala Krishna +2 more
doaj +1 more source
On Metric Dimensions of Symmetric Graphs Obtained by Rooted Product
Mathematics, 2018 Let G = (V, E) be a connected graph and d(x, y) be the distance between the vertices x and y in G. A set of vertices W resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in W.
Shahid Imran +3 more
doaj +1 more source
Recognizing clique graphs of directed and rooted path graphs
Discrete Applied Mathematics, 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Prisner, Erich, Szwarcfiter, Jayme L.
openaire +2 more sources
Rooted directed path graphs are leaf powers
Discrete Mathematics, 2010 Leaf powers are a graph class which has been introduced to model the problem of reconstructing phylogenetic trees. A graph \(G=(V,E)\) is called \(k\)-leaf power if it admits a \(k\)-leaf root, i.e., a tree \(T\) with leaves \(V\) such that \(uv\) is an edge in \(G\) if and only if the distance between \(u\) and \(v\) in \(T\) is at most \(k ...
Brandstädt, Andreas +3 more
openaire +2 more sources
The Graphs Whose Permanental Polynomials Are Symmetric
Discussiones Mathematicae Graph Theory, 2018 The permanental polynomial π(G,x)=∑i=0nbixn−i$\pi (G,x) = \sum\nolimits_{i = 0}^n {b_i x^{n - i} }$ of a graph G is symmetric if bi = bn−i for each i. In this paper, we characterize the graphs with symmetric permanental polynomials.
Li Wei
doaj +1 more source
Characterization of n-path graphs and of graphs having nth root
Journal of Combinatorial Theory, Series B, 1974 AbstractWe characterize connected graphs and digraphs having an nth root and so generalize results by A. Mukhopadhyay and D. P. Geller, respectively. We then define the n-path graph of a graph and characterize those graphs which are n-path graphs. This extends recent results by B. Devadas Acharya and M. N. Vartak. The corresponding problem for digraphs
Escalante, F, Montejano, L, Rojano, T
openaire +1 more source
A general approach to solving problems on graphs by collective automata
Труды Института системного программирования РАН, 2018 We propose a general method to solve graph problems by a set of automata (computational agents) located in vertices of undirected ordered connected rooted graph and communicating by passing messages along graph edges.
I. B. Burdonov, A. S. Kossatchev
doaj +1 more source
Statistics of paths on graphs with two heavy roots
, 2023 The paper considers the behaviour of the number of paths of length $N$ on graphs with two heavy roots. Such vertices can be entropic traps. Numerical analysis is carried out for graphs with different degrees of root vertices. In the symmetric case, a numerical analysis of the number of paths is performed.
openaire +2 more sources