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Different-distance sets in a graph [PDF]
Communications in Combinatorics and Optimization, 2019 A set of vertices $S$ in a connected graph $G$ is a different-distance set if, for any vertex $w$ outside $S$, no two vertices in $S$ have the same distance to $w$.
Jason T. Hedetniemi +3 more
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Three Constructions on Graphs and Distance-Based Invariants [PDF]
Mathematics Interdisciplinary Research, 2022 Many graphs are constructed from simpler ones by the use of operations on graphs, and as a consequence, the properties of the resulting constructions are strongly related to the properties of their constituents.
Mahdieh Azari
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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
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Al-Rafidain Journal of Computer Sciences and Mathematics, 2023 The new distance defined on a connected graph G contains of three terms: The ordinary distance between any two vertices in G, both the sum and the product of the two vertices' degrees, as this distance is more useful than the ordinary distance ...
Asmaa Aziz
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A Study on Discrete Mathematics: Sum Distance in Neutrosophic Graphs with Application [PDF]
Neutrosophic Sets and Systems, 2020 Distance is an important parameter in any networks/ graphs. The idea of strong sum distance in the fuzzy graph was introduced by Tom and Sunitha (2015).
Kousik Dasa +4 more
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On the distance spectra of m-generation n-prism graph
AKCE International Journal of Graphs and Combinatorics, 2022 The distance matrix of a simple connected graph G is [Formula: see text] where dij is the length of a shortest path between the ith and jth vertices of G. Eigenvalues of D(G) are called the distance eigenvalues of G. The m-generation n-prism graph or (m,
Fouzul Atik +2 more
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The Generalized Distance Spectrum of the Join of Graphs [PDF]
, 2020 Let G be a simple connected graph. In this paper, we study the spectral properties of the generalized distance matrix of graphs, the convex combination of the symmetric distance matrix D(G) and diagonal matrix of the vertex transmissions Tr(G) .
Alhevaz, Abdollah +3 more
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AKCE International Journal of Graphs and Combinatorics, 2020 The status of a vertex , denoted by , is the sum of the distances between and all other vertices in a graph . The first and second status connectivity indices of a graph are defined as and respectively, where denotes the edge set of .
Harishchandra S. Ramane +2 more
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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 +4 more
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Graphs with small diameter determined by their $D$-spectra [PDF]
, 2018 Let $G$ be a connected graph with vertex set $V(G)=\{v_{1},v_{2},...,v_{n}\}$. The distance matrix $D(G)=(d_{ij})_{n\times n}$ is the matrix indexed by the vertices of $G,$ where $d_{ij}$ denotes the distance between the vertices $v_{i}$ and $v_{j ...
Liu, Ruifang, Xue, Jie
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