On the extremal graphs for Second Zagreb Index with fixed number of vertices and cyclomatic number
نویسندگان
چکیده
منابع مشابه
graphs with fixed number of pendent vertices and minimal first zagreb index
the first zagreb index $m_1$ of a graph $g$ is equal to the sum of squaresof degrees of the vertices of $g$. goubko proved that for trees with $n_1$pendent vertices, $m_1 geq 9,n_1-16$. we show how this result can beextended to hold for any connected graph with cyclomatic number $gamma geq 0$.in addition, graphs with $n$ vertices, $n_1$ pendent vertices, cyclomaticnumber $gamma$, and minimal $m...
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Let the trunk of a graph G be the graph obtained by removing all leaves of G. We prove that, for every integer c ≥ 2, there are at most finitely many trunks of semiharmonic graphs with cyclomatic number c — in contrast to the fact established by the last two of the present authors in their paper Semiharmonic Bicyclic Graphs (this journal) that there are infinitely many connected semiharmonic gr...
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A set of vertices $S$ of a graph $G$ is called a fixing set of $G$, if only the trivial automorphism of $G$ fixes every vertex in $S$. The fixing number of a graph is the smallest cardinality of a fixing set. The fixed number of a graph $G$ is the minimum $k$, such that every $k$-set of vertices of $G$ is a fixing set of $G$. A graph $G$ is called a $k$-fixed graph, if its fix...
متن کاملThe augmented Zagreb index, vertex connectivity and matching number of graphs
Let $Gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity. Denote by $Upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$. In the classes of graphs $Gamma_{n,kappa}$ and $Upsilon_{n,beta}$, the elements having maximum augmented Zagreb index are determined.
متن کاملHyperenergetic Graphs and Cyclomatic Number
AMS Mathematics Subject Classification (2000): 05C50
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ژورنال
عنوان ژورنال: Miskolc Mathematical Notes
سال: 2022
ISSN: ['1586-8850', '1787-2405', '1787-2413']
DOI: https://doi.org/10.18514/mmn.2022.2382