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Geodesic Distance in Planar Graphs [PDF]

Nuclear Physics B, 2003
We derive the exact generating function for planar maps (genus zero fatgraphs) with vertices of arbitrary even valence and with two marked points at a fixed geodesic distance. This is done in a purely combinatorial way based on a bijection with decorated
Ambjørn, Ambjørn, Bousquet-Mélou, Bousquet-Mélou, Bouttier, Bouttier, Bouttier, Brézin, Chassaing, David, Delmas, Di Francesco, Di Francesco, Distler, E. Guitter, Eynard, Gelfand, J. Bouttier, Jimbo, Kawai, Kawamoto, Knizhnik, P. Di Francesco, Schaeffer, Staudacher, Tutte, Tutte, Tutte, Tutte   +28 more
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Leveraging Different Distance Functions to Predict Antiviral Peptides with Geometric Deep Learning from ESMFold-Predicted Tertiary Structures [PDF]

Antibiotics
Background: Machine learning models have been shown to be a time-saving and cost-effective tool for peptide-based drug discovery. In this regard, different graph learning-driven frameworks have been introduced to exploit graph representations derived ...
Greneter Cordoves-Delgado, César R. García-Jacas, Yovani Marrero-Ponce, Sergio A. Aguila, Gabriel Lizama-Uc   +4 more
doaj   +2 more sources

Signed distance in signed graphs [PDF]

Linear Algebra and its Applications, 2021
Signed graphs have their edges labeled either as positive or negative. Here we introduce two types of signed distance matrix for signed graphs. We characterize balance in signed graphs using these matrices and we obtain explicit formulae for the distance spectrum of some unbalanced signed graphs.
Shahul K. Hameed, T.V. Shijin, P. Soorya, K.A. Germina, Thomas Zaslavsky   +4 more
openaire   +2 more sources

Monophonic Distance in Graphs [PDF]

Discrete Mathematics, Algorithms and Applications, 2011
For any two vertices u and v in a connected graph G, a u – v path is a monophonic path if it contains no chords, and the monophonic distance dm(u, v) from u to v is defined as the length of a longest u – v monophonic path in G. A u – v monophonic path of length dm(u, v) is called a u – v monophonic. The monophonic eccentricity em(v) of a vertex v in G
Titus, P., Santhakumaran, A.P.
openaire   +3 more sources

Distance in stratified graphs [PDF]

Czechoslovak Mathematical Journal, 2000
A stratified graph is an ordered pair \((G,S)\), where \(G\) is an undirected graph and \(S\) is a partition of its vertex set \(V(G)\) into classes called strata. For any stratum \(X\) the concepts analogous to the basic concepts concerning distance may be defined, namely \(X\)-eccentricity, \(X\)-radius, \(X\)-diameter, \(X\)-center, \(X\)-periphery.
Chartrand, Gary, Hansen, Lisa, Rashidi, Reza, Sherwani, Naveed   +3 more
openaire   +1 more source

Distance labeling in graphs [PDF]

Journal of Algorithms, 2004
Summary: We consider the problem of labeling the nodes of a graph in a way that will allow one to compute the distance between any two nodes directly from their labels (without using any additional information). Our main interest is in the minimal length of labels needed in different cases.
Gavoille, Cyril, Peleg, David, Pérennes, Stéphane, Raz, Ran   +3 more
openaire   +3 more sources

Distance (signless) Laplacian spectrum of dumbbell graphs [PDF]

Transactions on Combinatorics, 2023
In this paper, we determine the distance Laplacian and distance signless Laplacian spectrum of generalized wheel graphs and a new class of graphs called dumbbell graphs.
Sakthidevi Kaliyaperumal, Kalyani Desikan   +1 more
doaj   +1 more source

Distance Domination and Distance Irredundance in Graphs [PDF]

The Electronic Journal of Combinatorics, 2007
A set $D\subseteq V$ of vertices is said to be a (connected) distance $k$-dominating set of $G$ if the distance between each vertex $u\in V-D$ and $D$ is at most $k$ (and $D$ induces a connected graph in $G$). The minimum cardinality of a (connected) distance $k$-dominating set in $G$ is the (connected) distance $k$-domination number of $G$, denoted ...
Hansberg, Adriana, Meierling, Dirk, Volkmann, Lutz   +2 more
openaire   +2 more sources

On Eccentricity Version of Zagreb Coindices [PDF]

Mathematics Interdisciplinary Research, 2021
The eccentric connectivity coindex has recently been introduced (Hua and Miao, 2019) as the total eccentricity sum of all pairs of non-adjacent vertices in a graph.
Mahdieh Azari
doaj   +1 more source

Szeged-type indices of subdivision vertex-edge join (SVE-join)

Main Group Metal Chemistry, 2021
In this article, we compute the vertex Padmakar-Ivan (PIv) index, vertex Szeged (Szv) index, edge Padmakar-Ivan (PIe) index, edge Szeged (Sze) index, weighted vertex Padmakar-Ivan (wPIv) index, and weighted vertex Szeged (wSzv) index of a graph product ...
Asghar Syed Sheraz, Binyamin Muhammad Ahsan, Chu Yu-Ming, Akhtar Shehnaz, Malik Mehar Ali   +4 more
doaj   +1 more source