# Search results for: Sandi Klavžar

Molecular Informatics > 38 > 11-12 > n/a - n/a

*G*. In the recent years, it has received considerable attention for determining the variations of its computation. Motivated by the method of computation of the traditional Wiener index based on canonical metric representation, we present the...

Graphs and Combinatorics > 2019 > 35 > 6 > 1555-1569

*G*, the exact distance-

*p*graph $$G^{[\natural p]}$$ G [ ♮ p ] has

*V*(

*G*) as its vertex set, and two vertices are adjacent whenever the distance between them in

*G*equals

*p*. We present formulas describing the structure of exact distance-

*p*graphs of the Cartesian, the strong, and the lexicographic product. We prove such formulas for the exact distance-2 graphs of direct products...

Aequationes mathematicae > 2019 > 93 > 6 > 1085-1109

Journal of Mathematical Chemistry > 2019 > 57 > 7 > 1868-1883

Indian Journal of Pure and Applied Mathematics > 2019 > 50 > 2 > 451-460

*G*is a UC graph with radius at least 3, then substituting a central vertex

*u*of

*G*with an arbitrary graph

*H*and connecting the vertices of

*H*to all neighbors of

*u*(in

*G*), yields a UC graph again. This construction extends several earlier ones and enables a simple argument...

Bulletin of the Malaysian Mathematical Sciences Society > 2019 > 42 > 4 > 1773-1789

*G*by Dominator and Staller. The players alternatively select a vertex of

*G*that was not yet chosen in the course of the game. Dominator wins if at some point the vertices he has chosen form a dominating set. Staller wins if Dominator cannot form a dominating set. In this paper, we introduce the Maker–Breaker domination number $$\gamma _{\mathrm{MB}}(G)$$...

Central European Journal of Operations Research > 2019 > 27 > 3 > 615-623

*k*-alliance in

*G*if (i) each vertex not in

*S*has a neighbor in

*S*and (ii) each vertex of

*S*has at least

*k*more neighbors inside

*S*than outside of it. The global defensive

*k*-alliance number of

*G*is the minimum cardinality among all global defensive

*k*-alliance in

*G*. In this paper...

Journal of Mathematical Chemistry > 2019 > 57 > 1 > 343-369

Journal of Applied Mathematics and Computing > 2019 > 60 > 1-2 > 253-264

*M*-polynomial of a graph

*G*is defined as $$\sum _{i\le j} m_{i,j}(G)x^iy^j$$ ∑ i ≤ j m i , j ( G ) x i y j , where $$m_{i,j}(G)$$ m i , j ( G ) , $$i,j\ge 1$$ i , j ≥ 1 , is the number of edges

*uv*of

*G*such that $$\{d_v(G), d_u(G)\} = \{i,j\}$$ { d v ( G ) , d u ( G ) } = { i , j } . Knowing the

*M*-polynomial, formulas for bond...

Journal of Combinatorial Optimization > 2018 > 36 > 4 > 1388-1410

*r*is called an

*r*-ASC graph. The

*r*-ASC index $$\theta _r(G)$$ θr(G) of a graph

*G*is the minimum number of vertices needed to be added to

*G*such that an

*r*-ASC graph is obtained that contains

*G*as an induced subgraph. It is proved that $$\theta _r(G)\le 2r$$ θr(G)≤2r holds for...

Bulletin of the Malaysian Mathematical Sciences Society > 2018 > 41 > 4 > 2141-2149

*G*, and let

*G*|

*v*mean that a vertex

*v*of

*G*is declared to be already totally dominated. A graph

*G*is total domination game critical if $$\gamma _\mathrm{tg}(G|v) < \gamma _\mathrm{tg}(G)$$ γtg(G|v)<γtg(G) holds for every vertex

*v*in

*G*. If $$\gamma _\mathrm{tg}(G) = k$$ γtg(G)=k , then

*G*is further called...

Bulletin of the Malaysian Mathematical Sciences Society > 2018 > 41 > 3 > 1671-1680

*G*is a graph, then $$\mathrm{sg}(G)$$ sg(G) is the cardinality of a smallest vertex subset

*S*, such that one can assign a fixed geodesic to each pair $$\{x,y\}\subseteq S$$ {x,y}⊆S so that these $$\left( {\begin{array}{c}|S|\\ 2\end{array}}\right) $$ |S|2 geodesics cover all the vertices...

Discrete Applied Mathematics > 2017 > 233 > C > 175-186

Aequationes mathematicae > 2018 > 92 > 3 > 497-513

*G*is the smallest integer

*k*such that the vertex set of

*G*can be partitioned into sets $$V_i$$ Vi , $$i\in [k]$$ i∈[k] , where each $$V_i$$ Vi is an

*i*-packing. In this paper, we investigate for a given triple (

*a*,

*b*,

*c*) of positive integers whether there exists a graph

*G*such that $$\omega (G) = a$$ ω(G)=a , $$\chi (G) = b$$ χ(G)=b...

Discrete Optimization > 2017 > 26 > C > 66-77

Journal of Mathematical Chemistry > 2018 > 56 > 1 > 69-80

*G*is a graph and $$\mathcal{P}$$ P is a partition of

*V*(

*G*), then the partition distance of

*G*is the sum of the distance between all pairs of vertices that lie in the same part of $$\mathcal{P}$$ P . This concept generalizes several metric concepts and is dual to the concept of the colored distance due to Dankelmann, Goddard, and Slater. It is proved that the partition distance...

Graphs and Combinatorics > 2017 > 33 > 4 > 665-672

*k*-dominating graph $$D_k(G)$$ D k ( G ) of a graph

*G*is defined on the vertex set consisting of dominating sets of

*G*with cardinality at most

*k*, two such sets being adjacent if they differ by either adding or deleting a single vertex. A graph is a dominating graph if it is isomorphic to $$D_k(G)$$ D k ( G ) for some graph

*G*and some positive integer

*k*. Answering a...

Discussiones Mathematicae Graph Theory > 2017 > 37 > 2 > 337-352

Discrete Mathematics > 2017 > 340 > 5 > 1110-1115

Discrete Applied Mathematics > 2017 > 217 > P3 > 613-621