Results 31 to 40 of about 1,116 (99)
Spectral Conditions for Graphs to be k-Hamiltonian or k-Path-Coverable
Discussiones Mathematicae Graph Theory, 2020 A graph G is k-Hamiltonian if for all X ⊂ V (G) with |X| ≤ k, the subgraph induced by V (G) \ X is Hamiltonian. A graph G is k-path-coverable if V (G) can be covered by k or fewer vertex disjoint paths.
Liu Weijun +3 more
doaj +1 more source
The chromatic sum of a graph: history and recent developments
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 30, Page 1563-1573, 2004., 2004 The chromatic sum of a graph is the smallest sum of colors among all proper colorings with natural numbers. The strength of a graph is the minimum number of colors necessary to obtain its chromatic sum. A natural generalization of chromatic sum is optimum cost chromatic partition (OCCP) problem, where the costs of colors can be arbitrary positive ...
Ewa Kubicka
wiley +1 more source
Discussiones Mathematicae Graph Theory, 2021 In this paper, we study a new distance parameter triameter of a connected graph G, which is defined as max{d(u; v)+d(v;w)+d(u;w) : u; v;w ∈ V }and is denoted by tr(G).
Das Angsuman
doaj +1 more source
Conditional resolvability in graphs: a survey
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 38, Page 1997-2017, 2004., 2004 For an ordered set W = {w1, w2, …, wk} of vertices and a vertex v in a connected graph G, the code of v with respect to W is the k‐vector cW(v) = (d(v, w1), d(v, w2), …, d(v, wk)), where d(x, y) represents the distance between the vertices x and y. The set W is a resolving set for G if distinct vertices of G have distinct codes with respect to W.
Varaporn Saenpholphat, Ping Zhang
wiley +1 more source
Simple expressions for the long walk distance
, 2012 The walk distances in graphs are defined as the result of appropriate transformations of the $\sum_{k=0}^\infty(tA)^k$ proximity measures, where $A$ is the weighted adjacency matrix of a connected weighted graph and $t$ is a sufficiently small positive ...
Bapat +14 more
core +1 more source
The hull number of an oriented graph
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 36, Page 2265-2275, 2003., 2003 We present characterizations of connected graphs G of order n ≥ 2 for which h+(G) = n. It is shown that for every two integers n and m with 11≤n−≤m≤(n2), there exists a connected graph G of order n and size m such that for each integer k with 2 ≤ k ≤ n, there exists an orientation of G with hull number G.
Gary Chartrand +2 more
wiley +1 more source
A cospectral construction for the generalized distance matrix
Special MatricesThe generalized distance matrix of a graph is a matrix in which the (i,j)\left(i,j)th entry is a function, ff, of the distance between vertex ii and vertex jj.
Friesen Ori +5 more
doaj +1 more source
Journal of Mathematics, Volume 2026, Issue 1, 2026.In this article, the first eccentricity connectivity coindex is introduced as ECI¯G=∑uv∉EGε2u+ε2v, in which ε(u) denotes the eccentricity of the vertex u in the simple connected graph G. Then, the exact expressions are obtained for the first eccentricity connectivity coindex of some graph products.
Suha Wazzan +2 more
wiley +1 more source
On resolving edge colorings in graphs
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 46, Page 2947-2959, 2003., 2003 We study the relationships between the resolving edge chromatic number and other graphical parameters and provide bounds for the resolving edge chromatic number of a connected graph.
Varaporn Saenpholphat, Ping Zhang
wiley +1 more source
On Domination Number and Distance in Graphs [PDF]
, 2014 A vertex set $S$ of a graph $G$ is a \emph{dominating set} if each vertex of $G$ either belongs to $S$ or is adjacent to a vertex in $S$. The \emph{domination number} $\gamma(G)$ of $G$ is the minimum cardinality of $S$ as $S$ varies over all dominating ...
Kang, Cong X.
core